Health Care Manage Sci
DOI10.1007/s10729-006-9006-3
The application of forecasting techniques to modeling emergency medical system calls in Calgary,Alberta Nabil Channouf·Pierre L’Ecuyer·
Armann Ingolfsson·Athanassios N.Avramidis
Received:20June2006/Accepted:1October2006
?Springer Science+Business Media,LLC2006
Abstract We develop and evaluate time-series models of call volume to the emergency medical service of a major Canadian city.Our objective is to offer simple and effective models that could be used for realistic simulation of the system and for forecasting daily and hourly call volumes.Notable features of the analyzed time series are:a positive trend,daily,weekly,and yearly seasonal cycles,special-day effects,and posi-tive autocorrelation.We estimate models of daily vol-umes via two approaches:(1)autoregressive models of data obtained after eliminating trend,seasonality,and special-day effects;and(2)doubly-seasonal ARIMA models with special-day effects.We compare the es-timated models in terms of goodness-of-?t and fore-casting accuracy.We also consider two possibilities for the hourly model:(3)a multinomial distribution for the vector of number of calls in each hour conditional on the total volume of calls during the day and(4)?tting a time series to the data at the hourly level.For our data, (1)and(3)are superior.
Keywords Emergency medical service·Arrivals·Time series·Simulation·Forecasting
N.Channouf·P.L’Ecuyer·A.N.Avramidis
DIRO,Universitéde Montréal,Montréal,Canada
A.Ingolfsson(B)
School of Business,University of Alberta,
Edmonton,Alberta T6G2R6,Canada
e-mail:armann.ingolfsson@ualberta.ca 1Introduction
Most cities in the developed world have organizations that provide Emergency Medical Service(EMS),con-sisting of pre-hospital medical care and transport to a medical facility.Demand for such services is increasing throughout the developed world,in large part because of the aging of the population.In the U.S.,EMS funding decreased following conversion of direct federal fund-ing to block grants to states[11,37]that have,in many cases,been used for purposes other than EMS.Tighter budgets make ef?cient use of resources increasingly important.Reliable demand forecasts are crucial input to resource use planning,and the focus of this paper is on how to generate such forecasts.
Almost all demand to EMS systems arrives by phone,through calls to an emergency number(911in North America).Calls that arrive to911are initially routed to EMS,?re,or police.Calls routed to EMS are then evaluated,which involves obtaining an address, determining the nature and importance of the incident, and possibly providing instructions to a bystander on the use of CPR or other?rst-aid procedures.Dispatch-ing an ambulance to the call,the next step,is a sepa-rate function that can occur partly in parallel with call evaluation.The crew of the dispatched vehicle(s)then begins traveling toward the scene of the call,where they assess the situation,provide on-site medical care, and determine whether transport to a medical facility is necessary(this is the case roughly75%of the time). Once at the medical facility,EMS staff remain with the patient until they have transferred responsibility for her or his care to a nurse or physician.The crew may then need to complete various forms before it becomes available to take new calls.
Health Care Manage Sci
The resource requirements per EMS call are on the order of a few minutes for call evaluation and dispatch, and on the order of an hour for an ambulance and its crew.The latter component is growing in many locations because of increased waiting times in hospital emergency rooms[13,14,33,34].
The primary performance measure for an EMS sys-tem is typically the fraction of calls reached within some time standard,from the instant the call was made.In North America,a typical target is to reach90%of the most urgent calls within9min.Although universal standards are lacking[28],the response time is typically considered to begin when call evaluation begins and end when an ambulance reaches the call address.Sec-ondary performance measures include waiting times on the phone before reaching a911operator;(for example, 90%in10s[29]or95%in5s[12]),average call eval-uation times,average dispatch times,and average time spent at hospital.
The main decisions that require medium-term call volume forecasts(a few days to a few weeks into the future)are scheduling decisions for call evaluators,dis-patchers,and,most importantly,ambulances and their crews.Longer-term call volume forecasts are needed for strategic planning of system expansion or reorga-nization.Shorter-term(intra-day)forecasts could be used to inform decisions about when to call in extra resources.
Service level standards for EMS systems are imper-fect proxies for the real goal of such systems,namely to save lives and prevent suffering(see[15]for a dis-cussion of models that attempt to quantify such goals more explicitly).Meeting these service-level standards is expensive,so it is a problem of substantial economic and social interest to manage EMS systems ef?ciently. Generally speaking,ef?ciency involves balancing qual-ity of service against system costs.An important input to this operational problem is the call volume.Uncer-tainty in future call volume complicates the process of determining levels of EMS staf?ng and equipment.It is therefore important to correctly model the stochastic nature of call volumes,and in particular,to make pre-dictions of future call volumes,including uncertainty estimates(via prediction intervals).
Operations researchers have been developing plan-ning models for EMS systems,as well as police and ?re services,since the1970s.Green and Kolesar[17] provide a recent perspective on the impact of this work. Swersey[35]surveys the academic literature on this topic and[16]provides an EMS-practitioner-oriented literature survey.EMS planning models include simula-tion models([20]and[22]are recent examples),analyt-ical queueing models(notably the hypercube queueing model,see Larson[24,25]),and optimization models
for location of facilities and units.All of these mod-
els require estimates of demand as input.Typically,
planning models assume that demand follows a Poisson
process—an assumption that is supported by both theo-
retical arguments[e.g.,19]and empirical evidence[e.g.,
18,39].However,empirical studies of demand for both
EMS and other services(notably Brown et al.[9])indi-
cate that the rate of the Poisson arrival process varies
with time and may be random.The work we report
in this paper is aimed at estimating the arrival rate
during day-long or hour-long periods.We elaborate in
Section3on how our estimates can be used to support
simulation and analytical studies that assume a Poisson
arrival process.
Goldberg[16]mentions that“the ability to predict
demand is of paramount importance”but that this area
has seen little systematic study.The work that has been
done can be divided in two categories:(1)models of
the spatial distribution of demand,as a function of
demographic variables and(2)models of how demand
evolves over time.In the?rst category,Kamenetsky
et al.[23]surveyed the literature before1982and pre-
sented regression models to predict EMS demand as
a function of population,employment,and two other
demographic variables.Their models successfully ex-
plained most of the variation in demand(R2=0.92) among200spatial units in southwestern Pennsylvania.
McConnell and Wilson[27]is a more recent article
from this category which focuses on the increasingly im-
portant impact of the age distribution in a community
on EMS demand.We refer the reader to Kamenetsky
et al.[23]and McConnell and Wilson[27]for further
relevant references.
This paper falls in the second category,of modeling
and forecasting EMS demand over time.EMS demand
varies strongly by time of day and day of week,for
example see Zhu et al.[39]and Gunes and Szechtman
[18].Past related work that attempts to forecast daily
EMS demand includes Mabert[26],who analyzed
emergency call arrivals to the Indianapolis Police
Department.He considered several simple methods
based on de-seasonalized data and found that one
of them outperforms a simple ARIMA model[7].
In a similar vein,Baker and Fitzpatrick[4]used
Winter’s exponential smoothing models to separately
forecast the daily volume of emergency and“routine”
EMS calls and used goal programming to choose the
exponential smoothing parameters.
Recent work on forecasting arrivals to call centers
from a variety of industries is also relevant.For the pre-
diction of daily call volumes to a retailer’s call center,
Andrews and Cunningham[3]incorporate advertising
Health Care Manage Sci
effects in an ARIMA model with transfer functions;their covariates are indicator variables of certain special days and catalog mailing days.Bianchi et al.[6]use an ARIMA model for forecasting daily arrivals at a tele-marketing center,compare against the Holt–Winters model,and show the bene?ts of outlier elimination.Tych et al.[36]forecast hourly arrivals in a retail bank call center via a relatively complex model with unob-served components named “dynamic harmonic regres-sion”and show that it outperforms seasonal ARIMA models;one unusual feature of their methodology is that estimation is done in the frequency domain.Brown et al.[9]develop methods for the prediction of the arrival rates over short intervals in a day,notably via linear regression on previous day’s call volume.
In this paper,we study models of daily and hourly EMS call volumes and we demonstrate their application using historical observations from Calgary,Alberta.Although we focus on the Calgary data,we expect the models could be used to model EMS demand in other cities as well and we will comment on likely similarities and differences between cities.
We have 50months (from 2000to 2004)of data from the Calgary EMS system.Preliminary analysis reveals a positive trend,seasonality at the daily,weekly,and yearly cycle,special-day effects,and autocorrelation.In view of this,we consider two main approaches:(1)autoregressive models of the residual error of a model with trend,seasonality,and special-day effects;and (2)doubly-seasonal ARIMA models for the residuals of a model that captures only special-day effects.Within approach (1),we explore models whose effects are the day-of-week and month-of-year.We also consider a model with cross effects (interaction terms)and a more parsimonious model,also with cross effects,but where
only the statistically signi?cant effects are retained.The latter turns out to be the best performer in terms of both goodness-of-?t and forecasting accuracy.All the models are estimated with the ?rst 36months of data and the forecasting error is measured with the data from the last 14months.We used the R and SAS statistical software for the analysis.
The remainder of the paper is organized as follows.Section 2provides descriptive and preliminary data analysis.In Section 3we present the different models of daily arrivals and compare them in terms of quality of ?t (in-sample)and forecast accuracy (out-of-sample).In Section 4,we address the problem of predicting hourly call volumes.Section 5offers conclusions.
2Preliminary data analysis
We have data from January 1,2000to March 16,2004,containing the time of occurrence of each ambulance call,the assessed call priority,and the geographical zone where the call originated.We work with the number of calls in each hour instead of their times of occurrence,to facilitate the application of time series models.We explain in the next section how such hourly counts can be related to a stochastic model of the times of individual arrivals.The average number of arrivals is about 174/day,or about 7/h.
Figure 1provides a ?rst view of the data;it shows the daily volume for year 2000.The ?gure suggests a pos-itive trend,larger volume in July and December,and shows some unusually large values,e.g.,on January 1,July 8,November 11,December 1;and low values,e.g.,on January 26,September 9.Figure 2shows monthly volume over the entire period.This plot reveals a clear
Fig.1The daily call volume for the year 2000.Some outliers appears in the plot
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Health Care Manage Sci
Fig.2The monthly call
volume over the entire period
450050005500
6000months
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positive trend;the likely explanation is a combination of population growth and aging in the city.Figure 3shows average volume by hour over the weekly cycle.The plot reveals a clear hour-of-day seasonality:over a 24-h cycle,higher call volumes are usually observed between 10a.m.and 8p.m.;substantially lower volumes are seen overnight.One also observes day-of-week effects.Closer inspection reveals,not surprisingly,in-creased activity during Friday and Saturday evening and early night.With respect to daily volume,larger values are observed over Friday and Saturday relative to the other days of the week.These observations would have to be taken into account when designing shift schedules for the ambulance crews.
Figures 4and 5give box-plots of the daily volume for each day of the week and monthly volume for each month of the year,respectively.Each box plot gives the
median,the ?rst and third quartiles (the bottom and top of the central box),the interquartile range (the height of the box),and two bars located at a distance of 1.5times the interquartile range below the ?rst quartile and above the fourth quartile,respectively.The small cir-cles denote the individual observations that fall above or below these two bars.We see again that Friday and Saturday have more volume than the average.July,December,and November are the busiest months (in this order)while April is the most quiet month.
3Models for daily arrivals
We now consider ?ve different time-series models for the arrival volumes over successive days.Although in the end we conclude that one of these models ?ts
Fig.3The average hourly call volume over the weekly cycle
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hours (24x7 days)
n u m b e r o f c a l l s
14385
127168
Mon.Tue.Wed.Thu.Fri.Sat.Sun.
Health Care Manage Sci Fig.4Box plots of arrival volumes per day for each day of the week
50100150200250
n u m b e r o f c a l l
s
Mon.Tue.Wed.Thu.Fri.Sat.Sun.
the Calgary data best,we discuss all of them because different models from the collection that we present may be appropriate depending on the city being studied and the purpose of the analysis.These models are de?ned and studied in Sections 3.1to 3.5.In Section 3.6,we compare these models in terms of both quality of ?t (in-sample)and forecast accuracy (out-of-sample).Throughout the paper,t denotes the time index in days and the number of arrivals on day t is denoted Y t ,for t =1,2,...,n ,where n =1,537.The models are ?tted to the ?rst 1,096observations (January 1,2000through December 31,2002),and the remaining 441observations are used for prediction (January 1,2003through March 16,2004).
There are compelling theoretical reasons to assume that call arrivals follow a nonhomogeneous Poisson process (NHPP).The Palm–Khintchine theorem [e.g.,10]states,approximately,that the superposition of arrival processes from many small and indepen-dent “sources”(patients,in an EMS context)is well-approximated by a Poisson process.The rate of this process will vary with time (because medical emergen-cies are more likely to occur at certain times)and the rate may not be known with certainty (because it may be in?uenced by factors other than time).
For purposes of illustration,suppose that arrivals during hour h follow a Poisson process with a random rate that remains constant during the hour.Conditional on the number of calls during the hour,call it Z h ,the arrival times of individual calls within the hour are independently and uniformly distributed between 0and 1.This is the “order statistic property”for a Poisson process and it holds regardless of whether the arrival rate is deterministic or random [see 32,Sections 4.5–4.6].Our models in this and the next section quantify the distribution of the daily arrival counts Y t and the
Fig.5Box plots of mean daily arrival volumes per month
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s
Jan.Feb.Mar.Apr.May Jun.Jul.Aug.Sep.Oct.Nov.Dec.
Health Care Manage Sci
hourly counts Z h .One can use the following procedure to simulate call arrival times on day t :
1.Simulate the daily count Y t .As we will see in this
section,this involves simulating the residual from a standard autoregressive process.
2.Given Y t ,generate the vector Z t of hourly counts
on day t .As we will see in the next section,this involves simulating a multinomial random https://www.doczj.com/doc/ff12739008.html,e the order statistic property to distribute the
simulated number of arrivals in each hour.If the arrival rate varies too rapidly to be approx-imated as constant over hour-long periods,then it is straightforward to modify our models to use shorter periods,for example half-hours.Thus,if one limits at-tention to this general and plausible NHPP model,then each of our models of arrival counts by period yield corresponding stochastic models of all the arrival times,which can support analytical and simulation studies.3.1Model 1:?xed-effect model with independent
residuals One would expect to see month-of-year and day-of-week effects in EMS demand in most cities.Our pre-liminary analysis of the Calgary data indicates a positive trend and con?rms the presence of month-of-year and day-of-week effects.This suggests the following linear model as a ?rst approximation:Y j ,k ,l =a +?βj +?γk +?αl +? j ,k ,l ,
(1)
where Y j ,k ,l is the number of calls on a day of type j
in month k of year l ,the parameters a ,?βj ,?γk ,and ?αl ,
are real-valued constants,and the residuals j ,k ,l are independent and identically distributed (i.i.d.)normal
random variables with mean 0.The preliminary analysis
suggests that for Calgary,the yearly effect is approxi-mately a linear function of l ,which allows us to express the model more conveniently as Y t =a +bt +
7 j =1
βj C t ,j +
12 k =1
γk S t ,k +E t ,(2)
where a ,b ,the βj ,and the γk are constants,the indica-tor C t ,j is 1if observation t is on the j th day of the week
and 0otherwise,the indicator S t ,k is 1if observation t is in the k th month of the year and 0otherwise.In other cities,it might be more appropriate to model the yearly effect as a nonlinear function of t .We assume that the residuals E t are i.i.d.normal with mean 0and variance σ2E ,0,i.e.,a Gaussian white noise process.Given the presence of the constant parameter a ,we impose the standard identi?ability constraints:
7 j =1
βj =
12 k =1
γk =0.(3)
(Without these constraints,there would be redundant parameters;for example,adding a constant κto all the βj ’s and subtracting κfrom a would give the same model.)We estimated the parameters for the regres-sion model (2)using least squares and obtained the residuals displayed in Fig.6,in which the circled points are at a distance larger than 3?σE ,0from zero,where ?σ2E ,0is the empirical variance of the residuals.There is a single residual larger than 4?σE ,0,which corresponds to January 1,2002,and seven other residuals larger than 3?σE ,0:December 1,2000;January 1,2001;May 27,2001;August 2,2001;September 8,2001;June 27,2002;July 12,2002.The single residual smaller than ?3?σE ,0is on July 30,2001.January 1appears to be
Fig.6The residuals E t for the simple linear model of Eq.2
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4
Time (days)
s t a n d a r d i z e d r e s i d u a l s
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Health Care Manage Sci
a special day,with a call volume systematically larger than average.The month of July also has a larger vol-ume per day than the other months(in the data).One potential explanation that we decided to consider is the Calgary Stampede,held every year in July.The Stam-pede includes one of the largest rodeos in the world and it is the most important annual festival in Calgary (https://www.doczj.com/doc/ff12739008.html,).The dates for this event are:July7–16,2000;July6–15,2001;July5–14,2002; and July4–13,2003.To account for those two types of special days,we add two indicator variables H t,1and H t,2to our model,where H t,1is1if observation t is on January1and0otherwise,whereas H t,2is1if obser-vation t is on one of the40Stampede days enumerated above,and0otherwise.This gives the model
Y t=a+bt+
7
j=1
βj C t,j+
12
k=1
γk S t,k
+ω1H t,1+ω2H t,2+E t,(4) in which we now have two additional real-valued para-metersω1andω2,and the residuals now have variance
σ2 E .The timing,nature,and number of such special
events will vary between cities but the same gen-eral approach can be used if the dates of the special events are known.We estimate all the parameters of this linear regression model by standard least-squares, using the?rst n=1,096observations.If we denote the parameter estimates by?a,?b,?βj,?γk,?ω1and?ω2,then the estimates of Y t and E t are given by
?Y
t=?a+?bt+
7
j=1
?β
j
C t,j+
12
k=1
?γk S t,k
+?ω1H t,1+?ω2H t,2(5) and
?E
t=Y t??Y
t.(6)
A naive estimator ofσ2
E would be the empirical
variance
?σ2E=1
n?s
n
t=1
?E2
t
,(7)
where s=21is the number of parameters estimated in the model.However,this variance estimator is biased if the residuals are correlated[5],and we will see in a moment that they are.
We must test the hypothesis that the residuals are a white-noise process,i.e.,normally distributed and uncorrelated with zero mean and constant variance. Stationarity and normality of the residuals is plausible, based on Fig.6and on Q–Q(quantile–quantile)plots not shown here.To test for autocorrelation,we use the Ljung-Box test statistic,de?ned by
Q=n(n+2)
l
i=1
?r2i
n?i
,
where n is the number of residuals,?r i is the lag-i sample autocorrelation in the sequence of residuals,and l is the maximum lag up to which we want to test the autocor-relations.Under the null hypothesis that the residuals are uncorrelated and n s,Q has approximately a chi-square distribution with l degrees of freedom.Here we have n=1,096and s=21.We apply the test with l= 30and obtain Q=154.8.The corresponding p-value is smaller than2.2×10?16,so the null hypothesis is clearly rejected.This strong evidence of the presence of correlation between the residuals motivates our next model.
3.2Model2:an autoregressive process for the errors of
Model1
We improve Model1by?tting a time-series model to the residuals E t.Since the E t process appears to be normal and stationary,it suf?ces to capture the auto-correlation structure.We do this with an autoregressive process of order p(an AR(p)process),de?ned by
E t=φ1E t?1+···+φp E t?p+a t,(8) where the a t are i.i.d.normal with mean zero and varianceσ2a.Based on the residuals de?ned by Eq.6, and using standard tools of model identi?cation[7,38], we?nd that p=3is adequate(different values of p will be appropriate for different cities).When estimating the coef?cientsφl in a model with p>3,we?nd that the coef?cientsφl for l>3are non-signi?cant at the 5%level.For example,the p-value of the t-test forφ4 is about0.153.
The model obtained by combining Eqs.4and8with p=3can be written alternatively as
φ(B)
?
?Y
t?a?bt?
7
j=1
βj C t,j
?
12
k=1
γk S t,k?ω1H t,1?ω2H t,2
=a t,(9)
whereφ(B)=1?φ1B?φ2B2?φ3B3,B is the back-shift operator de?ned by B p E t=E t?p,andφ1,φ2,φ3 are the autoregressive parameters.We estimate the parameters(a,b,β1,...,β7,γ1,...,γ12,ω1,ω2,φ1,φ2,φ3) by(nonlinear)least squares[1,page67],based on the observations Y t for t=4,...,n,where n=1096.
Health Care Manage Sci Table1Parameter estimates for Model2
Parameter a bω1ω2
Intercept Trend/month Jan.1Stampede
Estimate149.30.03160.5 2.7
St.error 3.30.00311.0 4.5
p-val.of t-test<0.001<0.001<0.0010.544
1β2β3β4β5β6β7
Mon.Tue.Wed.Thu.Fri.Sat.Sun. Estimate?4.2?5.0?5.3?0.98.57.6?0.8
St.error 2.5 2.5 2.5 2.5 2.5 2.5 2.5
p-val.of t-test0.0950.0460.0340.7190.0010.0020.747 Parameterγ1γ2γ3γ4γ5γ6γ7
Jan.Feb.Mar.Apr.May Jun.Jul. Estimate?5.6?4.1?2.5?4.00.5 4.113.2
St.error 2.9 2.8 2.8 2.8 2.7 2.8 2.9
p-val.of t-test0.0480.1520.3580.1490.8490.138<0.001 8γ9γ10γ11γ12
Aug.Sep.Oct.Nov.Dec.
Estimate?1.3?0.3?4.30.3 4.1
St.error 2.8 2.8 2.8 2.8 2.8
p-val.of t-test0.6270.9280.1210.9160.150
Parameterφ1φ2φ3σ2a
Estimate0.1920.1080.083250.1
St.error0.0300.0310.030–
p-val.of t-test<0.001<0.0010.006
The parameter estimates are given in Table1,to-
gether with their standard errors and the p-value of a
t-test of the null hypothesis that the given parameter
is zero,for each parameter.We then compute the
residuals?a t=?φ(B)(Y t??Y t)in a similar manner as for
Model1and we estimateσ2a by
?σ2a=1
n?s
n
t=4
?a2t,(10)
where n=1,096and s=24.This gives?σ2a=250.1. Figure7presents visual diagnostics for residual normal-ity:we see the estimated residual density and a normal Q–Q plot,i.e.,the empirical quantiles of normalized residuals plotted versus the corresponding quantiles of the standard normal distribution(with mean0and variance1).Figure8is a diagnostic for(lack of)residual autocorrelation:it shows the standardized residuals,the sample autocorrelations up to lag30,and the p-values of the Ljung-Box test for each lag.We conclude that the residuals a t appear to be white noise.Thus,Model2is a much better?t than Model1.
The most signi?cant parameters in Table1are a(the mean),b(the positive trend),ω1(the positive January 1effect),φ1,φ2,andφ3(the positive AR parameters),γ7(the positive July effect),andβ5andβ6(the positive Friday and Saturday effects).Other parameters signi?-cant at the10%level areβ1toβ3(the negative effects of Monday–Wednesday)andγ1(the negative effect of January).(Since April has the lowest average in Fig.5,
one may?nd it surprising that January has signi?cant negative coef?cient and not April.But the average for January becomes smaller after removing the January 1effect.Also,this estimation uses only the?rst1,096 days of data,whereas Fig.5combines all1,537days). This gives a total of13signi?cant parameters.We could eliminate the other ones;we will do that in Section3.4. Observe thatω2(the Stampede effect)is not signi?cant; most of the increased volume during the Stampede days is captured by the July effect.In fact,the average volume per day is about186during the Stampede days compared with180during the other days of July and 174on average during the year.
We can also use this model to estimate the variance of the residuals E t in Model1.Their sample variance (7)underestimatesσ2
E
=Var[E t]because they are pos-itively correlated.If we multiply both sides of Eq.8by E t and take the expectation,we get
σ2E=E[E2t]=φ1γ1+φ2γ2+φ3γ3+σ2a
=(φ1ρ1+φ2ρ2+φ3ρ3)σ2E+σ2a,
whereγi=Cov(E t,E t?i)andρi=Corr(E t,E t?i)for each i.Replacing all quantities in this last expression
by their estimates and resolving forσ2
E
,we obtain?σ2
E
=
291.8as an estimate ofσ2
E
.By comparing with the estimateσ2a=250.1,we see that Model1has about 17%more variance than Model2.
Health Care Manage Sci Fig.7Diagnostic for normality of residuals for Model
2
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50
Estimated density (kernel)
0.000
0.0050.0100.015
0.020
–3
–2–10123
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–2002040
60
Normal Q–Q Plot
Theoretical Quantiles
S a m p l e Q u a n t i l e
s
3.3Model 3:adding cross effects
We now extend Model 2by adding second-order terms to capture the interaction between the day-of-week and month-of-year factors.We simply add the term
7 j =112 k =1
δj ,k M t ,j ,k
(11)
to the right side of Eq.4and subtract the same term inside the brackets in Eq.9,where the indicator vari-
able M t ,j ,k is 1if observation t is on the j th day of the week and k th month of the year.This introduces the additional model parameters δj ,k ,which must satisfy the
identi?ability constraints
12k =1δj ,k =0for each j and 7
j =1δj ,k =0for each k .
We found that the estimates for the parameters βj ,γk ,and ωi in this model were almost the same as in Model 2.Table 2gives the estimated values of the parameters that differ from those of Model 2,together with the p -value of a t -test that the given parameter is zero.The estimated variance of the residuals has
Fig.8Diagnostic for (lack of)residual autocorrelation for Model 2
Standardized Residuals
Time
0200400
6008001000
–3024
0510********
0.00.40.8
Lag
A C F
ACF of Residuals
24
6810
0.00.40.8p values for Ljung–Box statistic
Lag
p v a l u e
Health Care Manage Sci Table2Parameter estimates for Model3
Mon.Tue.Wed.Thu.Fri.Sat.Sun.
Parameterδ1,1δ2,1δ3,1δ4,1δ5,1δ6,1δ7,1Jan. Est.?0.3 5.0 4.6?6.9 4.0?6.3?0.2
St.error 3.9 4.0 4.0 4.2 4.2 4.2 4.2
p-val.of t-test0.9420.2100.2560.1020.3390.1370.965 Parameterδ1,2δ2,2δ3,2δ4,2δ5,2δ6,2δ7,2Feb. Est.?5.4 5.6 3.7?3.6 1.0 2.9?4.2
St.error 4.2 4.1 4.2 4.2 4.2 4.2 4.2
p-val.of t-test0.1930.1730.3820.3860.8050.4860.321 Parameterδ1,3δ2,3δ3,3δ4,3δ5,3δ6,3δ7,3Mar. Est.8.1 6.2?3.7 6.20.5?12.3?4.9
St.error 4.1 4.2 4.1 3.9 3.9 4.2 4.2
p-val.of t-test0.0520.1370.3640.1130.8910.0030.240 Parameterδ1,4δ2,4δ3,4δ4,4δ5,4δ6,4δ7,4Apr. Est. 1.7?3.70.4 4.2?3.3 4.1?3.4
St.error 4.2 4.2 4.2 4.2 4.2 3.9 3.9
p-val.of t-test0.6860.3690.9270.3140.4340.2870.393 Parameterδ1,5δ2,5δ3,5δ4,5δ5,5δ6,5δ7,5May Est. 5.6?0.8?0.50.1?6.6?1.8 4.0
St.error 3.8 3.9 3.9 4.2 4.2 4.2 4.2
p-val.of t-test0.1430.8400.9080.9860.1130.6630.345 Parameterδ1,6δ2,6δ3,6δ4,6δ5,6δ6,6δ7,6Jun. Est.?2.6?4.5?1.311.5?6.7 3.00.7
St.error 4.1 4.1 4.2 3.8 3.9 4.2 4.2
p-val.of t-test0.5250.2760.7470.0030.0830.4680.875
1,7δ2,7δ3,7δ4,7δ5,7δ6,7δ7,7
Est.?3.9?4.6 1.50.2 6.6 1.8?1.6
St.error 3.9 4.2 4.2 4.2 4.2 3.8 3.9
p-val.of t-test0.3240.2690.7280.9540.1120.6490.685
1,8δ2,8δ3,8δ4,8δ5,8δ6,8δ7,8
Est. 6.1 4.7?1.4?0.8?3.10.1?5.4
St.error 4.2 3.9 3.9 3.9 4.2 4.2 4.2
p-val.of t-test0.1420.2270.7110.8330.4520.9860.195
1,9δ2,9δ3,9δ4,9δ5,9δ6,9δ7,9
Est.?1.6?5.3?4.5?2.3 2.9 4.9 5.9
St.error7.1 6.8 6.7 6.7 5.4 5.87.9
p-val.of t-test0.8190.4410.5020.7320.5940.3990.457
1,10δ2,10δ3,10δ4,10δ5,10δ6,10δ7,10
Est.0.9?1.5?3.7?6.8 3.20.87.1
St.error 4.0 4.0 4.2 4.2 4.2 4.2 3.9
p-val.of t-test0.8220.7020.3710.1050.4360.8390.073
1,11δ2,11δ3,11δ4,11δ5,11δ6,11δ7,11
Est.?1.20.17.8?2.2 4.5?5.4?3.5
St.error 4.3 3.9 3.9 3.9 4.1 4.1 4.6
p-val.of t-test0.7750.9820.0440.5780.2800.1870.444
1,12δ2,12δ3,12δ4,12δ5,12δ6,12δ7,12
Est.?7.3?1.1?2.70.4?3.18.2 5.7
St.error 4.3 4.3 4.2 4.2 3.9 3.9 4.0
p-val.of t-test0.0920.7970.5180.9240.4170.0360.154
Parameterφ1232a
Est.0.2130.1260.085241.5
St.error0.0300.0310.031–
p-val.of t-test<0.001<0.0010.006
Health Care Manage Sci Fig.9Diagnostic for the normality of residuals,Model 3
–50
50
Estimated density (kernel)
0.000
0.0050.0100.015
0.020
–3
–2–10123
–40
–2002040
60
Normal Q–Q Plot
Theoretical Quantiles
S a m p l e Q u a n t i l e
s
been reduced to σ2
a =241.5,about 4%less than for Model 2.The diagnostics for the residuals are in Fig.9.The Ljung-Box test does not detect correlation in the residuals (we have n =1,096,get Q =5.394,and the p -value of the test is 0.944)(Fig.10).
The slightly better ?t of this model compared with Model 2is obtained at the expense of a much larger number of parameters and several of these parameters do not appear to be signi?cant.The next step is to remove them.
3.4Model 4:considering only the signi?cant parameters
This model is a stripped-down version of Model 3,in which we keep only the parameters that are signi?cant at the 10%level (i.e.,for which the p -value of the t -test in Table 1or 2is less than 0.10).In Table 2,eight para-meters δj ,k and three parameters φi are signi?cant at the 90%level.There are ten other signi?cant parameters in Table 1,for a total of 20.With the identi?ability
Fig.10Diagnostic for the correlation between residuals,Model 3
Standardized Residuals
Time
0200400
6008001000
–2024
0510********
0.00.40.8
Lag
A C F
ACF of Residuals
24
6810
0.00.40.8p values for Ljung–Box statistic
Lag
p v a l u e
Health Care Manage Sci
Table 3Parameter estimates for Model 4Parameter a
b
ω1Intercept Trend/month Jan.1Estimate 149.60.03257.8St.error
1.9
0.00310.7p -val.of t -test <0.001<0.001<0.001Parameter β1β2β3β5β6Mon.Tue.Wed.Fri.Sat.Estimate ?4.3?5.3?6.27.87.9St.error
1.5 1.4
1.4
1.4
1.5
p -val.of t -test 0.004<0.001<0.001
<0.001<0.001
Parameter γ1γ7Jan.Jul.Estimate ?5.712.4St.error
2.9 2.7
p -val.of t -test 0.050<0.001Parameter
δ1,3δ6,3δ4,6δ5,6δ7,10δ3,11δ1,12δ6,12Mon.Sat.Thu.Fri.Sun.Wed.Mon.Sat.Mar.Mar.Jun.Jun.Oct.Nov.Dec.Dec.Estimate 7.9?11.112.0?7.18.38.5?7.88.2St.error
4.2 4.3 3.9 3.9 3.8 4.0 4.5 4.1p -val.of t -test 0.0600.0100.0020.0690.0290.0340.0830.046
Parameter φ1φ2φ3σ2a Estimate 0.2120.1320.094241.6St.error
0.0300.0310.031–
p -val.of t -test
<0.001
<0.001
0.002
constraints,there remain s =15independent parame-ters out of those 20.The same strategy of including only the signi?cant parameters from Model 3could be used in other cities,but the set of signi?cant parameters will vary between cities,of course.We reestimate the model with those parameters only (all other parameters are set at zero)and obtain the values given in Table 3.All these parameters are signif-icant.The most signi?cant interaction parameters δj ,k are for Saturday in March (negative interaction)and
Fig.11Diagnostic for the normality of residuals,Model
4
–500
50
Estimated density (kernel)0.000
0.0050.0100.015
0.020–3–2–10123
–40–200204060
Normal Q–Q Plot
Theoretical Quantiles
S a m p l e Q u a n t i l e
s
Health Care Manage Sci Fig.12Diagnostic for the correlation between residuals,Model 4
Standardized Residuals
Time
0200400
6008001000
–2024
0510********
0.00.40.8
Lag
A C F
ACF of Residuals
24
6810
0.00.40.8p values for Ljung–Box statistic
Lag
p v a l u e
Thursday in June (positive interaction).Other mildly signi?cant interactions,at the 10%level,are (by order of signi?cance)Saturday in December,Wednesday in November,Monday in March,Sunday in October,Fri-day in June,and Monday in December.
The estimated variance of the residuals is σ2
a =241.9.The diagnostics for the residuals are in Figs.11and 12.The Ljung-Box test does not detect correlation in the residuals (we have n =1,096,get Q =11.581,and the p -value of the test is 0.48).
3.5Model 5:a doubly-seasonal ARIMA process We now consider a different model:an ARIMA model with two seasonal cycles.We decompose our time series as
Y t =N t +ω1H t ,1+ω2H t ,2,
(12)
where {N t }is modeled as a doubly-seasonal ARIMA process and the other components capture the special days (January 1and Stampede days).Given the season-ality patterns across the weekly and yearly cycle implied by the analysis in Section 2,we propose an ARIMA model with two seasonal cycles:a weekly cycle,with period s 1=7,and an approximate annual cycle,with period s 2=365.This choice of periodicities means that the conditional mean of N t is regressed on N t ?365;for example,January 1,2004is regressed on January 1,2003.In other words,after eliminating February 29
(which we did),this regression “aligns”the same dates across years.
The general form of a doubly-seasonal ARIMA model with periods s 1and s 2is [7,8,38]:
φ(B ) s 1(B s 1) s 2(B s 2)?d ?d 1s 1
?d 2
s 2N t
=θ(B ) s 1(B s 1) s 2(B s 2)a t ,(13)
where ?d
s =(1?B s )d ,φ, s 1, s 2,θ, s 1,and s 2are polynomial functions of order p ,p 1,p 2,q ,q 1,and q 2,respectively,and {a t }is a Gaussian white noise process.This model is referred to as an ARIMA (p ,d ,q )×(p 1,d 1,q 1)s 1×(p 2,d 2,q 2)s 2process.
We follow a standard model-building protocol to identify the model (choice of the polynomial orders and exponents d ,d 1,and d 2),estimate the parameters (ω1,ω2,and the polynomial coef?cients),and perform diag-nostic checks [7,38].ARIMA models with more than one seasonal cycle are dif?cult to estimate in general,because the multiple seasonalities complicate Eq.13with several operators,due to the multiplicative nature of the expressions involved.A concrete selection cri-terion must be adopted for model selection.Here,we used Akaike’s information criterion (AIC),discussed in Section 3.6.We keep the model with minimum AIC,subject to non-rejection of the null hypothesis that model residuals are a white-noise process [7].Based on this criterion,we identify the following model for N t :
(1?φ7B 7?φ14B 14?φ28B 28)(1?φ365B 365)(1?B )N t
=(1?θ1B )a t .
(14)
Health Care Manage Sci Table4Parameter estimates,Model5
Parameterω1ω2
Jan.1Stampede
Estimate43.816.6
St.error12.0 3.8
p-val.of t-test<0.001<0.001
Parameterφ7φ14φ28φ365θ1σ2a Estimate0.0640.1030.0820.1280.905251.7 St.error0.030.030.030.040.01–
p-val.of t-test0.0380.0010.0070.001<0.0001
The parameters are estimated jointly via least squares based on Eqs.12and14,i.e.,we?nd the parameter val-ues that minimize the sum of squares of the estimated residuals.The estimates are given in Table4,together with their p-values.Note that Model5has considerably fewer parameters than the other models.It is also inter-esting to observe that for this model,the parameterω2 (Stampede days effect)is highly signi?cant,in contrast with Models2to4.The explanation is that there is no “July effect”term in the model.
3.6Model comparison:Goodness of?t and forecast
performance
In this section,we compare the?ve models in terms of their quality of?t and forecasting performance.The results are in Table5.
With respect to quality of?t,we report the standard error of model residuals,?σa,the number s of parameters estimated,and Akaike’s information criterion(AIC, see Akaike[2]and Wei[38,page153]).The AIC has the advantage of taking into account both the mean-square error of the residuals and the number of esti-mated parameters in the model.It is designed to be an approximately unbiased estimator of the Kullback–Leibler distance(or cross-entropy or relative entropy)between the true model and?tted model.It is de?ned by
AIC(s)=n ln(?σ2a)+2s,(15) where n is the number of observations,s is the number of estimated parameters in the model,and?σ2a is the maximum likelihood estimator of the variance of resid-uals,which is approximately the same as the sample variance(10)under the assumption that the residuals are i.i.d.normal[30].Bias-reduced variants known as the AICC are discussed,e.g.,in[8,pages301–304].
A model with minimal AIC is a good compromise between parsimony and small(empirical)variance of the residuals.
The models of Sections3.1–3.5were?tted to the ?rst1,096days of data.We then used the estimated models to forecast for the remaining441days(t= 1,097,...,1,537),at forecast lag ranging from1day ahead to21days ahead.The lag- forecast error at day t is de?ned as
e t( )=Y t+ ??Y t( ),
where?Y t( )is the forecast of Y t+ based on the informa-tion available on day t.Forecasts for doubly-seasonal ARIMA processes obey fairly complicated recursive formulas;see,for example,Brockwell and Davis
Table5Comparison of models for daily arrivals
Model1Model2Model3Model4Model5
?σ2a291.8250.1241.5241.6251.7 St.error of?t?σa17.0815.8115.5415.5515.87 s212490157 Degrees of freedom10751072100610811088 AIC(s)6099619460456068
RMSE(1)17.8215.3815.3113.9115.68 MRAE(1)(in%)7.58 6.14 6.14 5.72 6.91
Health Care Manage Sci Fig.13Forecast RMSE(s )for Models 1–5,for forecast lags =1,...,21
1214
1618
20Horizon
R M S E
123456789101112131415161718192021
model 1 model 2 model 3 model 4 model 5
[8,pages 175-182],but forecasting software facilitates their computation.
Commonly used forecast-accuracy metrics are the Root Mean Square Error (RMSE)and the Mean Rel-ative Absolute Error (MRAE)at various forecast lags,de?ned in our case as
RMSE ( )= 1442? 1538? t =1097e 2t
( )and MRAE ( )=
1
442? 1538? t =1097|e t ( )|Y t +
.for lag .The MRAE standardizes each forecasting error term by the corresponding process value Y t + ,to re?ect the idea that larger numbers usually require less absolute accuracy;it must be used with caution because it may be in?ated substantially by a few moderate absolute errors that correspond to very small values |Y t + |.
Table 5summarizes the model evaluation.The upper part of the table collects information on the ?t with the data used for the estimation (the ?rst 36months).
It recalls the estimated variance of the residuals,?σ2
a ,then its square root ?σa called the standard error of ?t ,the number s of independent estimated parameters,the number n ?s of degrees of freedom,and the AIC (s )
criterion (for Model 1,?σ2
a is replaced by ?σ2E ,de?ned at the end of Section 3.2).According to the AIC criterion,Model 4is the winner,followed by Model 5and then Model 2.It must be underlined,however,that Model 5was selected by minimizing the AIC over a class of ARIMA models,so the AIC measure is biased to its advantage.
The second part of the table gives the RMSE and MRAE for the forecasts of lag 1.The RMSE for lags 1to 21are displayed in Fig.13.For small lags,Model 4is clearly the best model in terms of forecast accuracy,followed by Models 2and 3.For lags s ≥13(approx-imately),RMSE (s )is about the same for all models except Model 5,whose forecasts are much noisier.En-couragingly,the AIC measure at the estimation stage has successfully identi?ed the best model.
In interpreting the standard error of ?t and the RMSE,it is helpful to recall from our preliminary data analysis that the average number of calls per day was about 174.If calls were generated by a stationary Pois-son process with a rate of 174/day,then the standard deviation of the number of calls per day would be √
174=13.2.The Model 4RMSE with a lag of 1comes close to this value.This suggests that,given knowledge of call volumes up to a certain point in time,the Poisson arrival rate for the next 24h is almost deterministic.The RMSE for longer lags is higher,suggesting that when modeling arrivals more than one day into the future,one should view them as being generated by a Poisson process with a random arrival rate.The discussion at the beginning of this Section outlines how one can quantify the distribution for the arrival rate.
4Modeling hourly arrivals
Now that we have a good model of day-by-day call volumes,we turn to the modeling of hour-by-hour call volumes.We will denote the number of calls during hour h by Z h ,where h =1,...,24n and n =1,537.We investigate two modeling and forecasting approaches.
Health Care Manage Sci Both build on a model for the daily call volume Y t and
add to that model a component that divides the daily
volume across the24h of the day.Our?rst approach is
via the conditional distribution of the vector of number
of calls in each hour,given the total daily call volume.
The second approach?ts a time-series model directly
to the data at the hourly level.
4.1Model6:modeling the conditional distribution
Here we use Model4for the daily arrival volumes,
then assume that on day t,the conditional distribution
of the vector Z t=(Z24(t?1)+1,...,Z24t),given Y t,is
independent of what happens on days other than t.A
simple candidate for this conditional distribution is a
multinomial distribution with parameters(N,p1,...,
p24),where N=Y t.Each p i represents the probability
that a randomly selected call arriving during the day
arrives in hour i.The vector(p1,...,p24)is called
the daily pro?https://www.doczj.com/doc/ff12739008.html,e of the multinomial distribution
implies that the hours of occurrence of different calls
on day t are independent,conditional on Y t.
Figure3suggests that different days of the week
should have different daily pro?les;for instance,Fri-
days and Saturdays have a very different pro?le than
the other days.Based on a more detailed analysis of
our data,we regrouped the days of the week into four
daily pro?le categories:(1)Monday–Wednesday,(2)
Thursday and Sunday,(3)Friday,and(4)Saturday.
Each category c has a different daily pro?le vector
(p c,1,...,p c,24)for category c,for c=1,2,3,4.The
probability p c,i is estimated as the fraction of calls in
category c that occur in hour i,i.e.,
?p c,i=
n
t=1
Z24(t?1)+i P t,c
t=1
h=1
Z24(t?1)+h P t,c
,(16)
for i=1,2,...,24,where the indicator variable P t,c is 1if day t is in category c and0otherwise.A positive aspect of this model is that the model for Y t remains exactly the same as before.We could also use other distributions than the multinomial for the conditional distribution of Z t.
One way of testing the goodness-of-?t of this model is as follows.Under the multinomial assumption,condi-tional on Y t and if day t is in category c,the chi-square statistic
Q t=
24
i=1
(Z24(t?1)+i?Y t p c,i)2
Y t p c,i
should have approximately the chi-square distribution with23degrees of freedom if Y t p c,i is large enough (e.g.,larger than5)for all i[31].So we could compute these Q t’s for all days and compare their empirical distribution to the chi-square distribution.But it turns out that Y t p c,i is often rather small(less than5)for the night hours.For this reason,before applying the test we regrouped four early morning hours,from3:00a.m. to7:00a.m.,in a single period.All other hours count for one period each.This gives m=21periods and the expected number of calls in each period is at least?ve under the multinomial model.The probability that a call is in period i on a day of category c is then
?p c,i=
?
?
?
p c,i for i=1,2,3,
p c,4+p c,5+p c,6+p c,7for i=4,
p c,i+3for i=5, (21)
(17)
Let?Z t,i be the number of calls in period i of day t. We have
m
i=1
?Z
t,i=Y t.For a day of category c,con-ditional on Y t,our multinomial(null)hypothesis now states that?Z t=(?Z t,1,...,?Z t,m)has the multinomial distribution with parameters(Y t,?p c,1,...,?p c,m).To es-timate the parameters?p c,i,we use the consistent esti-mators??p c,i obtained simply by summing the?p c,i’s of category4appropriately and using the correct hour-to-period correspondence as in Eq.17.Then,for large enough n,the Pearson test statistic
Q m?1,t=
m
i=1
(?Z t,i?Y t??p c,i)2
Y t??p c,i
,(18)
should have approximately the chi-square distribution with m?1=20degrees of freedom under the multino-mial model.
We computed the1,537values of Q m?1,t for our data, and compared their empirical distribution(distribution A)to the chi-square distribution(distribution C)via a Q–Q plot.Having found a bit of discrepancy in the right tail,we thought that perhaps the chi-square distribution is not a good enough approximation of the exact distri-bution of Q m?1,t under the multinomial model,so we also generated(by simulation)a times series of1,537 successive realizations of Y t under Model4,then a sample of vectors?Z t conditional on Y t under the multi-nomial distribution hypothesis,and computed the cor-responding values of Q m?1,t,for t=1,...,1,537.The empirical distribution of this sample is called distribu-tion B.Figure14shows a Q–Q plot of distribution A against distribution B.The?t is excellent except in the right tail.The observations in the right tail correspond to days where the observed daily pro?le differed signif-icantly from the usual daily pro?le for that type of day. This could be due to unusual(perhaps unpredictable) events that happened on those days.This has occurred on Sunday October29,2000,Monday March19,2001, Friday April13,2001,Monday September30,2001,
Health Care Manage Sci Fig.14Q–Q plot of the empirical distribution A against the empirical
distribution B of a sample of Q m ?1,t generated from Model 6under the
multinomial assumption
102030
4050
10203040
50Generated
O b s e r v e d
Sunday October 28,2001,Saturday October 28,2002,Saturday May 21,2003,and on January 1of each year.For January 1,the different pro?le could be predicted because it happens every year.We conclude that even though the ?t is not perfect in the right tail,it is gen-erally good enough to justify the use of the multino-mial model in practice,in particular for purposes of forecasting.
We now turn to forecasting hourly volumes with this model.If h is the i th hour of day t ,a forecast of Z h made days before day t (at the end of day t ? ,so =1means at the beginning of day t )is simply
?p
c ,i ?Y t ? ( ),where ?Y t ? ( )is the forecast of Y t as de?ne
d in Section 3.6and c is th
e category for day t .
To forecast Z h on the day that hour h occurs,we
could use ?p
c ,i ?Y t ?1(1),but we shoul
d b
e able to do better by taking into account the information we have in addition to the call volume o
f the previous days,i.e.,the call volume on day t ,up to hour h ?1.For example,suppose that at 11:00a.m.we want call volume forecasts for each of the next 13h.We assume we already know the number of calls durin
g the ?rst 11
h of the day.If W t ,11is that number,then a naive idea would be to estimate the remaining call volume on day
t as ?Y
t ?1(1)?W t ,11and then use ?p
c ,i (?Y t ?1(1)?W t ,11)?p
c ,12+···+?p c ,24(19)
as a forecast for the i th hour,for i >11.This is a bad
idea because a larger W t ,11results in a smaller forecast for the rest of the day,suggesting a negative correlation
between the volumes over the different hours of the
day.In reality,the correlation is typically positive.
Let W t ,i =Z 24(t ?1)+1+···+Z 24(t ?1)+i be the num-ber of calls during the ?rst i hours of day t .Under
our model,?Y
t =?Y t ?1(1)is a suf?cient statistic for the information from previous https://www.doczj.com/doc/ff12739008.html,ing Bayes’formula,
the conditional distribution of Y t given ?Y t and W t ,i is P
Y t =y |?Y
t ,W t ,i =w =
P W t ,i =w |Y t =y P
Y t =y |?Y t
P W t ,i =w |?Y
t (20)
for all integers 0≤w ≤y .The distribution of W t ,i conditional on Y t =y is binomial with parameters
(y ,p c ,1:i ),where p c ,1:i =
i =1p c , .Even though Y t can only take integer values,Model 4approximates its
distribution conditional on ?Y
t by a normal with mean ?Y t and variance σ2
Y =Var [φ?1(B )(a t )].This could be used to write down a speci?c expression for the probabilities in Eq.20and computing them numerically.For Y t ,the probability of any integer value y can be approximated by integrating the normal density over the interval [y ?1/2,y +1/2].Note that conditional on W t ,i and Y t ,the vector (Z t ,i +1,...,Z t ,24)has a multinomial distribu-tion with parameters (Y t ?W t ,i ,p c ,i +1/(1?p c ,1:i ),...,p c ,24/(1?p c ,1:i )).
For forecasting,we may only need the conditional
expectation E [Y t |?Y
t ,W t ,i ]instead of the entire distri-bution (20).If we assume that the pair (Y t ,W t ,i )has approximately a bivariate normal distribution,which is close to the truth under our model when p c ,1:i is not to
Health Care Manage Sci
close to 0or 1and Y t has a large enough expectation,then we have [21,page 93]:
E Y t |?Y
t ,W t ,i =w
=?Y t +Cov [Y t ,W t ,i |?Y t ]Var [W t ,i |?Y
t ]×(w ?E [W t ,i |?Y
t ]).(21)
But E [W t ,i |?Y
t ]=p c ,1:i ?Y t ,Cov [Y t ,W t ,i |?Y t ]=p c ,1:i σ2
a ,
and
Var [W t ,i |?Y
t ]=E Y t [Var [W t ,i |?Y t ,Y t ]]+Var Y t [E [W t ,i |?Y
t ,Y t ]]=?Y t p c ,1:i (1?p c ,1:i )+p 2c ,1:i σ2a .
Combining this with Eq.21,we obtain E [Y t |?Y
t ,W t ,i =w ]=?Y t +w ?p c ,1:i ?Y
t (1?p c ,1:i )?Y t /σ2a +p c ,1:i
.(22)
We will see the results of applying this formula later in
this section.
4.2Model 7:an extension of Model 4with an
hour-of-day effect We write this model as Z h =p c ,i Y t +W h
if h is the i th hour of day t and c is the category for day t ,where the process Y t obeys one of the previous day-to-day models and the process W h is AR (q )for some q .
If Y t obeys Model 4,for instance,then the variance σ2a of the residuals in that model would have to be
reduced,to account for the additional variance coming
from the W h ’s.This gives the following:Z h =p c ,i
?Y
t +E t
+24 l =1
αl D h ,l +W h ,(23)
where D h ,l =1if h is the l -th hour of the day and 0otherwise,and {E t }and {W h }are AR processes.
An important distinction between Models 6and 7is the following.With Model 6,there is positive correla-tion between the arrivals counts in different hours of the same day,regardless of the distance between those hours,and the only correlation between the hours of two successive days is due to the autocorrelations in the process E t .With Model 7,on the other hand,the correlation between hours on the same day decreases with the distance between them and there is also an additional correlation between hours on two successive days but that are close in time (e.g.,Friday evening and Saturday morning hours).
When we estimate the model,we add the two
constraints 24
l =1αl =0and 24t h =24(t ?1)+1W h =0,for t =1,...,n ,and we force {E t }to be an AR(3)process as in models for days.We estimated the process {W h }.The largest (observed)lag for which the autoregressive parameter was signi?cant at the 5%level is lag 44,but few autoregressive parameters for lags larger than 25were signi?cant at the 1%level.For this reason,we decided to retain an AR(25)model for W h and an AR(3)model for E t .We reestimated the model in Eq.23with these constraints.This is our Model 7.With it,we obtained a standard error of ?t of 3.6.The residuals diagnostic is shown on Fig.15.
Fig.15Diagnostic for residual normality,hourly Model
7
–20
–10
10
20
Estimated density (kernel)
0.00
0.020.040.06
0.0
8
–4
–2024
–10
–5051015
Normal Q–Q Plot
Theoretical Quantiles
S a m p l e Q u a n t i l e s
Health Care Manage Sci
4.3Comparison of Models 6and 7
We compare the forecasting performance of Models 6and 7by measuring the root mean square error (RMSE)at different lags in the 441days for t =1,097,...,1,537.For h =24(t ?1)+1,...,24t ,we de?ne the lag-r error
at hour h by e h (r )=Z h +r ??Z
h (r ),where ?Z h (r )is the forecast of Z h +r based on the selected model.We consider two cases:
(1)For the forecasts of the 24coming hours of day t
when we are at the beginning of day t and have ?Y
t as a forecast of Y t from Model 4,we measure the error by
RMSE (r )=
14411536 t =1096e 224(t ?1)(r );(2)For the forecasts of the hours i =12,...,24of day
t after having observed the ?rst 11hours,using the formula (22)to update the forecast of Y t for Model 6,we measure the error by
RMSE (r )=
14411537
t =1097e 224(t ?1)+11(r ).Table 6gives a representative subset of the results.Overall,Model 6outperforms Model 7for both Cases (1)and (2);its RMSE is never larger and it is often clearly smaller.For a very short horizon of 1h,it is not surprising that the two models perform about the same,because they both catch the relatively strong correla-tion between two successive hours.For longer horizons,they also perform about the same,presumably because the true correlation is not very strong in that case.But for the values of r in between (horizons of a few hours),Model 6clearly performs better.For example,if we are at 11:00a.m.(we have observed W t ,11)and want to predict the volume of calls between 4:00and 5:00p.m.on the same day (6h ahead),the RMSE is 3.7
for Model 7compared to 2.3for Model 6.We also see the bene?t of using information about the call volume during the early hours of the day when forecasting for the latter part of the day.For example,using Model 6at 11:00a.m.to forecast the call volume between 4:00and 5:00p.m.,the RMSE is 3.5if we ignore the call volume from midnight to 11:00a.m.but it drops to 2.3if we incorporate this information.
5Conclusion
We have considered a variety of time series models for estimating and forecasting daily and hourly EMS call volumes.EMS demand is in?uenced by when people work,commute,sleep,and celebrate,and our models attempt to capture these in?uences at least in part via yearly,weekly,and daily seasonal cycles,as well as special treatment of New Year’s day and the Stampede,the most important festival in the city we studied.
We used three basic approaches for daily call vol-umes:standard regression ignoring dependencies,re-gression models with correlated residuals,and a third approach (doubly-seasonal ARIMA)that takes into ac-count a speci?c cross-effect dependency structure at the start and captures the correlations between residuals as well.The usual interpretation of these models is that the ?rst deterministic part captures the seasonal and non-seasonal components,and the second stochastic part (errors)captures the effect of omitted or non-observable effects such as serial correlation.We ?nd that a model from the second category,that includes a selected subset of signi?cant day-of-week main effects,month-of-year main effects,and interaction terms,per-forms best when forecasting 1or 2days into the fu-ture.The advantage of this model over the standard regression model decreases as the length of the forecast horizon increases,and disappears at around 2weeks.
Table 6RMSEs by origin and horizon for the two hourly models
Horizon r
Model 6Model 7Case (1):
12(11:00–12:00a.m.) 3.1 3.5Forecasts of Z 24(t ?1)+r to Z 24t ,14(1:00–2:00p.m.) 3.1 3.9at time h =24(t ?1)
17(4:00–5:00p.m.) 3.5 3.923(10:00–11:00p.m.) 3.1 3.224(11:00–12:00p.m.) 3.2 3.3Case (2):
1(11:00–12:00a.m .) 3.1 3.1Forecasts of Z 24(t ?1)+11+r to Z 24t ,3(1:00–2:00p.m.) 2.9 3.5at time h =24(t ?1)+11
6(4:00–5:00p.m .) 2.3 3.712(10:00–11:00p.m.) 3.1 3.213(11:00–12:00p.m.)
3.1
3.1
Health Care Manage Sci
The doubly-seasonal ARIMA model performed poorly when forecasting more than a week into the future.
For hourly call volumes,we used two approaches: one built around the conditional distribution of hourly volumes,conditional on the daily volume,and another that?ts a time-series model to the hourly data.Both approaches can be combined with any of the daily call volume models that we investigated,and we illus-trated its use with the best-performing daily call volume model.We also showed how one could compute intra-day forecast updates,which could be useful for real-time staf?ng decisions.We found that the conditional distribution approach generally worked better.We demonstrated that updating hourly forecasts using call volume from the early part of the day can improve fore-cast accuracy considerably,at least for certain hours of the day.
The models we present are simple and practical, and could be used for routine forecasting for an EMS system,as well as in simulation models of such sys-tems.Our models that combine regression and ARMA processes showed an improvement over pure seasonal ARIMA.We also demonstrated the importance of modeling the effects of special days,day-of-week,and month-of-year.
Although we expect that the general approach de-scribed in this paper should be applicable in other cities, it is important to investigate whether this is the case. In future research,it would be interesting and useful to develop models that forecast the spatial distribution of demand,not only based on time but also on demo-graphic variables.
Acknowledgements This work has been supported by NSERC-Canada Grants no.ODGP-0110050and CRDPJ-251320,a grant from Bell Canada via the Bell University Laboratories,and a Canada Research Chair to P.L’Ecuyer as well as NSERC-Canada Grant no.203534to A.Ingolfsson.We thank the Cal-gary EMS department(particularly Heather Klein-Swormink and Tom Sampson)for making this work possible,J.Cheng, E.Erkut,D.Haight,and T.Riehl for useful discussions and assistance with data preparation,and the anonymous referees for useful comments.
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SCI收录期刊影响因子排名表 Mechanical & Manufacturing Engineering 058 Engineering, Industrial Ranking Journal Title Impact Factor # 1 JOURNAL OF PRODUCT INNOV A TION MANAGEMENT 1.038 # 2 ERGONOMICS 0.749 # 3 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT 0.635 # 4 JOURNAL OF QUALITY TECHNOLOGY 0.608 # 5 IIE TRANSACTIONS 0.445 # 6 INTERNA TIONAL JOURNAL OF INDUSTRIAL ERGONOMICS 0.387 7 ISSUES IN SCIENCE AND TECHNOLOGY 0.368 # 8 RELIABILITY ENGINEERING & SYSTEM SAFETY 0.302 9 R&D MAGAZINE 0.017 059 Engineering, Manufacturing Ranking Journal Title Impact Factor 1 COMPOSITES PART A-APPLIED SCIENCE AND MANUFACTURING 0.689 2 PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART B-JOURNAL OF EN 0.262 3 IEEE TRANSACTIONS ON COMPONENTS PACKAGING AND MANUFACTURING TECHNOLOGY PA RT 0.241 4 IEEE TRANSACTIONS ON COMPONENTS PACKAGING AND MANUFACTURING TECHNOLOGY PA RT 0.241 061 Engineering, Mechanical Ranking Journal Title Impact Factor # 1 JOURNAL OF AEROSOL SCIENCE 1.378 # 2 AEROSOL SCIENCE AND TECHNOLOGY 1.342 # 3 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS 0.984 # 4 INTERNA TIONAL JOURNAL OF PLASTICITY 0.901 # 5 PROGRESS IN ENERGY AND COMBUSTION SCIENCE 0.786 6 COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 0.727 # 7 INTERNA TIONAL JOURNAL OF HEA T AND MASS TRANSFER 0.690 # 8 WEAR 0.686 9 J OURNAL OF ENGINEERING MECHANICS-ASCE 0.666 # 10 EXPERIMENTS IN FLUIDS 0.636 11 JOURNAL OF HEA T TRANSFER-TRANSACTIONS OF THE ASME 0.537 # 12 TRIBOLOGY TRANSACTIONS 0.522 # 13 INTERNA TIONAL JOURNAL OF MECHANICAL SCIENCES 0.509 # 14 TRIBOLOGY INTERNA TIONAL 0.450
八口语测试 1 口语的特点 ●交互性：口语交际是交际双方或多方的活动，通过交际各方相互交流传递信息。 ●即时性: 口语活动一般要求参与者对谈话对方的言语立即作出反应（包括回答问 题、补充、反对、赞成、延续等）。由于这种反应具有即时性，说话者来不及精心 准备话语，因此话语中多有迟疑、停顿、口误、冗余成分等。 ●副语言因素: 口语中说话者往往借助语调、重音、音量等副语言手段来增加表达效 果。 ●非语言因素: 说话者在说话时常借助手势、目光、表情等体势语来表情达意。 ●与听的不可分割性: 除了自言自语、演讲、口授等，一般场合下的口语活动是在“… 听→说→听→说…”的过程中进行的。 2 口语能力的构成 Weir & Bygate (1992) 将口语能力分为微语言技能（micro-linguistic skills）、常规技能（routine skills）和应变技能（improvisation skills）三个层次。 ●微语言技能（micro-linguistic skills） ◆Accuracy in phonology, grammar, lexis, etc. ●常规技能（routine skills） ?Information routines ◆Expository routines: narration, description, instruction, comparison, etc. （expository essay, expository writing：说明文） ◆Evaluative routines: explanations, predictions, justifications, preferences, decisions, etc. ?Interaction routines ◆Sequences of turns: telephone conversations, interviews, conversations at parties, etc. ●应变技能（improvisation skills） ?Negotiation of meaning ◆Level of explicitness: Speakers need to choose an appropriate level of explicitness, taking into account what the listener knows and can accommodate; ◆Procedures of negotiation: speakers need to be concerned about selecting an appropriate level of specificity in the light of listener response, including use of paraphrase, metaphor, choice of general of specific lexical items, conversational adjustments to contact and ensure understanding, and repetition and clarification procedures. ?Management of interaction ◆Agenda management: referring to co ntrol over the content (participants’ right to choose the topic, or introduce topics they want to talk about) and control over the development or duration of a topic; ◆Turn-taking: knowing how to signal that one wants to speak, recognizing the right moment to get a turn, how not to lose one’s turn, recognizing other people’s signals of desire to speak, knowing how to let other persons have a
SCI收录材料期刊影响因子及排名（一） 自然 Nature Science 科学 Nature Material 自然（材料）Nature Nanotechnology 自然（纳米技术）Progress in Materials Science 材料科学进展Nature Physics 自然（物理）Progress in Polymer Science 聚合物科学进展Surface Science Reports 表面科学报告Materials Science & Engineering 材料科学与工程报告R-reports Angewandte Chemie-International 应用化学国际版Edition Nano Letters 纳米快报Advanced Materials 先进材料 Journal of the American Chemical 美国化学会志Society Annual Review of Materials Research 材料研究年度评论Physical Review Letters 物理评论快报Advanced Functional Materials 先进功能材料Advances in Polymer Science 聚合物科学发展
Biomaterials 生物材料 Small 微观 Progress in Surface Science 表面科学进展 Chemical Communications 化学通信 MRS Bulletin 材料研究学会（美国） 公告 Chemistry of Materials 材料化学 Advances in Catalysis 先进催化 Journal of Materials Chemistry 材料化学杂志 Carbon 碳 Crystal Growth & Design 晶体生长与设计 Electrochemistry Communications 电化学通讯 The Journal of Physical Chemistry B 物理化学杂志，B 辑： 材料、表面、界面与生物物理 Inorganic Chemistry 有机化学 Langmuir 朗缪尔 Physical Chemistry Chemical Physics 物理化学 International Journal of Plasticity 塑性国际杂志 Acta Materialia 材料学报 Applied Physics Letters 应用物理快报 Journal of power sources 电源技术
模拟试题一 个人信息介绍：(机问人答） 1. A: What’s your name, please? B: My name is ______. 2.A: Where do you study? B. I study at NO.1 senior middle school. 3.A: What subjects do you study? B: I study Chinese, Math, English, Physics, Chemistry, Biology, PE and so on. 4. A.:What subject do you like best? B: As far as i am concerned ,i like English best. 场景1：安排旅行计划(机问人答） 旅行行程单 目的地：西藏 交通工具：飞机 出发日期：5月2日 所需费用：2000元左右 所需行李：衣服、药品、照相机等 1.A: Where do you plan to go? B: I pan to go to Tibet. 2.A: How do you go there ? B: I will go there by plane.
3.A: When do you set off? B: I will set off on May 2nd. 4.A: What luggage do you need to take? B: I need to take some clothes,some medicine as well as a camera. 5.A: How much will the trip cost ? B: The trip will cost about 2000 RMB. 6.A: Which places have you been to already and where do you plan to go next? Why? B: I have been to Shanghai, Nanjing,Suzhou and so on. And i plan to go to Hainan next, for i love the sea so much. 7.A: How do you often go travelling by plane or by train? B: I often go travelling by train, as it is a cheap way to travel. 8.A: Do you think it is a good time to travel during the Spring Festival? B: I don’t think so. After all ,there will be too many people during the Spring Festival. I don’t like the crowds and noises. 场景2：去邮局寄包裹（人问机答） 包裹单 目的地： 包裹重量： 邮寄方式： 包裹内容： 付费方式：
2010年SCI收录材料期刊影响因子及排名 首次分享者：梦中浮萍已被分享4次评论(0)复制链接分享转载举报 Nature 自然31.434 Science 科学28.103 Nature Material 自然（材料）23.132 Nature Nanotechnology 自然（纳米技术）20.571 Progress in Materials Science 材料科学进展18.132 Nature Physics 自然（物理）16.821 Progress in Polymer Science 聚合物科学进展16.819 Surface Science Reports 表面科学报告12.808 Materials Science & Engineering R-reports 材料科学与工程报告12.619 Angewandte Chemie-International Edition 应用化学国际版10.879 Nano Letters 纳米快报10.371 Advanced Materials 先进材料8.191 Journal of the American Chemical Society 美国化学会志8.091 Annual Review of Materials Research 材料研究年度评论7.947 Physical Review Letters 物理评论快报7.180 Advanced Functional Materials 先进功能材料 6.808 Advances in Polymer Science 聚合物科学发展 6.802 Biomaterials 生物材料 6.646 Small 微观？ 6.525 Progress in Surface Science 表面科学进展 5.429 Chemical Communications 化学通信 5.34 MRS Bulletin 材料研究学会（美国）公告 5.290 Chemistry of Materials 材料化学 5.046 Advances in Catalysis 先进催化 4.812 Journal of Materials Chemistry 材料化学杂志 4.646 Carbon 碳 4.373 Crystal Growth & Design 晶体生长与设计 4.215 Electrochemistry Communications 电化学通讯 4.194 The Journal of Physical Chemistry B 物理化学杂志，B辑：材料、表面、界面与生物物理4.189 Inorganic Chemistry 有机化学 4.147 Langmuir 朗缪尔 4.097 Physical Chemistry Chemical Physics 物理化学 4.064 International Journal of Plasticity 塑性国际杂志 3.875 Acta Materialia 材料学报 3.729 Applied Physics Letters 应用物理快报 3.726 Journal of power sources 电源技术 3.477 Journal of the Mechanics and Physics of Solids 固体力学与固体物理学杂志 3.467 International Materials Reviews 国际材料评论 3.462 Nanotechnology 纳米技术 3.446 Journal of Applied Crystallography 应用结晶学 3.212
口语考试机考指南 机考当天，每场考试监考老师不得少于两人。一人负责计算机操作，其他监考老师负责监控学生是否有夹带或者使用手机进行作弊。一旦发现作弊，口试成绩记为0分。 1.考前准备：考生清单，格式如下表1。U盘或移动硬盘，用于拷贝学生的考试录音。考 试结束后老师们带回录音，交换听评。同时将音频文件夹以“考试时间+考试班级”命名，存在教研室电脑指定位置，之后将统一刻成光盘，作为教学资料存档。提供给学生抽签用的小纸条。建议多做一些。 2.设备检查：机考前，学生全部进入教室，落座，戴好耳机，打开话筒。教师打开语音 授课系统，依次点击学生，请他们说话确认话筒及耳机正常。如有发现有故障的座位，要求学生将耳机摘下，将所在位置的液晶显示器翻转，以表明此位置不可用于考试。（设备检查每次考试只需在考前做一次即可，不需要每考一个班都检查一次） 3.登记座位：设备检查完毕之后，学生按实际可使用的机器数，进入考场落座。教师依次 点击每个落座学生，询问姓名，座位号等信息，并相应登记入表格中。 4.抽取（随机分发）考题，同时登记每个考生所抽取的题目号。考生有1-2分钟的准备时 间。 5.点击考试-点击口语考试-1人考试-点选存储位置，新建文件夹，命名为考试班级名称， 确定，举手，示意考生考试即将开始。按下开始考试，将手放下，示意考生开始答题。 6.考生答题：考试答题时，需要在录音一开始报自己的学号，姓名，班级和抽取的题目。 而后开始正式考试。考生务必将麦打开。考试结束，摘下耳机，坐在位置上。直到老师示意可以离场。考试过程中，监考老师应及时巡视。发现有考生作弊，立即取消考试资格，口试成绩记为0分。 7.考生离场：在最后一名考生放下耳机后。监考老师按下考试结束。系统将在刚才建立的 文件夹中自动生成以座位号命名的wav格式的音频文件。监考老师可以点击阅卷，随机抽取几个考生，确保录音有效。随后示意考生将耳机挂好，离开。 8.下一场考生进场，重复步骤3-7. 9.考试结束后，将本次考试班级的所有录音资料用移动存储工具带走，交换阅卷。 以下为软件操作步骤：
中考英语听力口语自动化考试问答 一、听力口语自动化考试与以往考试相比有哪些主要变化 1.考试内容实行两考合一。将以往的英语口语等级测试和中考听力测试合并进行，通过计算机一次性完成考试。 2.考试方式实行人机对话。以往的英语口语等级测试方式为“师生对话”，由测试员现场提问，现场测试打分，以往的中考听力考试则在中考笔试时进行，依靠考场内广播或录音机播放听力磁带。实行人机对话后，考生坐在计算机前，戴上考试专用耳麦，由计算机播放听力录音和试题，考生用计算机作答并对着麦克风回答口语题。出题、考试、判卷、结果反馈全部由计算机完成。 3.成绩评定实行电脑评分。考试结束后，由计算机记录下考生的答案，由自动阅卷专用服务器综合各种特征给出评分，经考试组织部门确认后发布。 综上三点，听力口语自动化考试，简化了考试程序，减轻了考生负担，规范了考试要求，避免了人为因素可能造成的不利影响。 二、听力口语自动化考试如何组织 根据省教育厅统一部署，2009年起，全省中考英语听
力口语自动化考试由省教育厅统一组织，统一命制试题、统一考点设置、统一考试时间、统一考试流程、统一评分标准、统一发布成绩。 三、听力口语自动化考试考点和考场如何设置 人机对话考试对考点的要求比较高。省教育厅要求原则上以各初中学校为考点，以各学校的计算机网络机房为考场，考场计算机及相关软硬件配置均须符合考试所要求的基本条件，不符合要求的必须在升级、补充到位的基础上才能申报考点。从目前申报情况看，我市大多数初中学校已符合考场设置条件，全市大多数初中毕业生都可在本校参加听力口语自动化考试。少数不符合考场设置条件学校的学生由各地教育行政部门统一安排到就近的考点参加考试。 四、一个考场内同时有30人进行听力口语考试，会不会互相干扰 按照考场设置要求，一个考场内设置不少于33台考试机和1台监考机，每个考场同时安排30人进行考试。考试所用耳麦和话筒都是特制的，考生只能听到考试机播放的声音，话筒也只对定向的声音录音，完全不影响考试效果。2007年5月开始，省教育厅在苏州、南通、连云港部分学校进行过试点，实践证明效果良好，不会出现考生互相干
Mark Rank Abbreviated Journal Title (linked to full journal information) ISSN 2003 Total Cites Impact Factor Immediacy Index 2003 Articles Cited Half- life 1 PEDIATRICS 0031- 4005 25691 3.781 0.633 657 6.9 2 J AM ACAD CHILD PSY 0890- 8567 10771 3.779 0.532 171 7.1 3 MENT RETARD DEV D R 1080- 4013 676 3.479 0.788 33 3.4 4 PEDIATR RES 0031- 3998 8946 3.064 0.555 256 7.2 5 J PEDIATR 0022- 3476 19133 2.913 0.631 268 >10.0 6 J CHILD ADOL PSYCHOP 1044- 5463 701 2.487 0.233 43 4.2 7 PEDIATR INFECT DIS J 0891- 3668 6924 2.262 0.511 276 6.0 8 ARCH PEDIAT ADOL MED 1072- 4710 3905 2.190 0.719 153 4.9 9 PEDIATR CLIN N AM 0031- 3955 1850 1.926 0.091 77 7.5 10 PEDIATR PULM 8755- 6863 3124 1.917 0.261 161 5.6 11 DEV MED CHILD NEUROL 0012- 1622 4433 1.898 0.257 136 8.9 12 PEDIATR TRANSPLANT 1397- 3142 633 1.767 0.221 95 3.4 13 MED PEDIATR ONCOL 0098- 1532 2763 1.737 0.170 171 5.8 14 ARCH DIS CHILD 0003- 9888 10688 1.722 0.347 418 8.8 15 BIRTH-ISS PERINAT C 0730- 7659 615 1.709 0.357 28 6.4 16 J DEV BEHAV PEDIATR 0196- 206X 1285 1.699 0.289 45 8.8 17 J ADOLESCENT HEALTH 1054- 139X 2669 1.674 0.477 109 6.2
襄阳市中考口语测试样题（讨论稿） 说明： 1. 口语测试的时间在15分钟以内； 2. 本谈论稿参考了其它地区以及湖北省英语口语等级考试题型； 3. 增加口语测试是落实英语课程标准以及培养学生学科核心素养要求的需要，有利于引导教师按语言学习规律去教，引导学生按语言学习规律去学，有利于促进学生综合语言运用能力的提高。 样题 第一节：短文朗读（共1小题，5分） （计算机语音和屏幕文字提示）在本节，你将有60 秒钟的时间阅读屏幕上的短文，并作朗读准备。当听到“请开始录音”的提示后，请在90 秒钟内朗读短文一遍。 现在请开始准备。 （屏幕上显示英语短文以及60秒钟准备时间进度条） Dear Liu Ying, I’m glad to get a letter from you. You asked me something about British food. Now, I’m going to tell you what I usually eat every day. I usually have bread and eggs for breakfast. Mom prepares milk for me and tea for Dad. Seventy percent of students have lunch at school. The school dining hall has different kinds of food. My favorite food for lunch is sandwiches. I don’t like hamburgers. Some of students take lunchboxes to school. In the boxes there are usually sandwiches, biscuits and some fruit. Supper is the most important meal in a day from Monday to Friday. Mom cooks very good dishes. We often have meat and vegetables. But at weekends, our biggest meal is in the middle of the day. I also like Chinese food. Please write to tell me something about it! Yours, Tom （计算机语音和屏幕文字提示）现在请开始朗读、录音。 （计算机给出提示后开始朗读，屏幕上显示90秒钟录音时间进度条）（计算机语音提示）朗读、录音到此结束。 第二节：情景提问（共5小题，每小题1分，共5分） （计算机语音和屏幕文字提示）在本节，请你根据屏幕上提供的情景及提问内容要点，提出5个问题。每个问题你有20秒钟的思考和提问时间。 你的同桌刚度完假。于是你向他询问有关情况。请使用屏幕上的信息提出5个问题。 现在请开始提问。
全球材料类SCI收录期刊影响因子排名 期刊英文名中文名影响因子 Nature自然 Science科学 Nature Material自然（材料） Nature Nanotechnology自然（纳米技术） Progress in Materials Science材料科学进展 Nature Physics自然（物理） Progress in Polymer Science聚合物科学进展 Surface Science Reports表面科学报告 Materials Science & Engineering R-reports材料科学与工程报告 Angewandte Chemie-International Edition应用化学国际版 Nano Letters纳米快报 Advanced Materials先进材料 Journal of the American Chemical Society美国化学会志 Annual Review of Materials Research材料研究年度评论 Physical Review Letters物理评论快报 Advanced Functional Materials先进功能材料 Advances in Polymer Science聚合物科学发展 Biomaterials生物材料 Small微观？ Progress in Surface Science表面科学进展 Chemical Communications化学通信 MRS Bulletin材料研究学会（美国）公告 Chemistry of Materials材料化学 Advances in Catalysis先进催化 Journal of Materials Chemistry材料化学杂志 Carbon碳 Crystal Growth & Design晶体生长与设计 Electrochemistry Communications电化学通讯 The Journal of Physical Chemistry B物理化学杂志，B辑：材料、表面、界面与生物物理Inorganic Chemistry有机化学 Langmuir朗缪尔 Physical Chemistry Chemical Physics物理化学 International Journal of Plasticity塑性国际杂志 Acta Materialia材料学报 Applied Physics Letters应用物理快报 Journal of power sources电源技术 Journal of the Mechanics and Physics of Solids固体力学与固体物理学杂志 International Materials Reviews国际材料评论 Nanotechnology纳米技术
启明英语听说计算机考试系统 1.1 概述 英语听说计算机考试系统是一套采用现代化计算机技术辅助实现听说考试的系统。与传统的考生直接面对考官的口语考考试方式不同，代之以考生面对计算机，由计算机向考生显示和播放预先录制好的考试题目，考生在计算机面前回答问题，计算机录制并收集考生的答题录音，而后集中由评判教师统一评分。计算机辅助听说考试系统有以下特点： 大规模考生可以同时进行考试； 考试、评卷分离； 考官发音标准，每个考生听到的声音都是一样的； 考试题型丰富多样。 这套考试系统方案，我们根据听说考试的特点，充分融入了启明电子多年在教育行业积累的经验和先进的技术与理念。 1.2 系统业务模型 1.2.1 英语听说计算机考试的概念 考生信息：用于验证和区分每一个参加考试的考生的信息表。一般包括考号、姓名、考点、试室等。 试题信息：由试题制作功能模块生成的试题文件包。这是一套完整试题的文件的集合。 开考指令：在所有的考前准备工作完毕后，监考员就可以启动系统的开始考试指令。随后考试系统将在预先设好的时间间隔内，依次播放考题的内容，考生根据提示录制答案。考生的考试是在统一的指令下完成的。 数据打包：考试完毕后，以考生为单位打包答案，经加密、压缩后的考生答案传输到服务器端；当本场考试结束后，所有考生的答案压缩包又打包成一个以试室为单位的压缩包，以便于传输或刻录，将来评卷也是以试室为单位。 1.2.2 工作流程 听说考试具有时间短、规模大、数据保密性强的特点，必须严格按操作流程来进行。所有监考的教师，考试前一定要进行适当的培训，以掌握听说考试的操作过程。具体工作流程如下：1.2.3 模块结构 模块组成结构如下图所示：
随着研究生报名人数的逐年增加，研究生复试一般改为差额复试，考生复试的成绩如何直接影响到其是否被录取。研究生复试一般分为专业课复试与英语复试，而英语复试主要是口语测试。由于从2005年起研究生入学考试英语笔试部分取消了听力，因此，研究生复试中除了传统的口语测试外，很多学校增加了听力部分。这里我们特别邀请了中央财经大学多年的博士生、硕士生与MBA英语复试考官冯玉红和温剑波老师，为大家介绍一下研究生英语复试的备考。 随着研究生报名人数的逐年增加，研究生复试一般改为差额复试，考生复试的成绩如何直接影响到其是否被录取。研究生复试一般分为专业课复试与英语复试，而英语复试主要是口语测试。由于从2005年起研究生入学考试英语笔试部分取消了听力，因此，研究生复试中除了传统的口语测试外，很多学校增加了听力部分。这里我们特别邀请了中央财经大学多年的博士生、硕士生与MBA英语复试考官冯玉红和温剑波老师，为大家介绍一下研究生英语复试的备考。 一般性备考：总结常见热门话题 英语口试备考：考前提前了解考试形式 专业备考：不必担心专业词汇太少 听力备考：不建议听英语考试的听力材料 口试评分标准：分项打分与整体打分 无论参加哪种形式的口语考试，说一口流利、准确的英语都是通过考试的关键所在。因此，语言的基本功与长期的口语素材积累至关重要。一般性备考可以分为下面几个部分： 1..应试材料的准备：为了准备口语考试，可以准备一些材料，如
《英语中级口语教程》、《四、六级英语口语应试》等。当然如果确定参加哪种英语口试，又了解其口语考试的形式与内容，选择针对其考试的口语材料更为有效，如雅思口语、托福口语等。 2. 制定复习计划：根据备考时间与所要参加的口试类型制定复习计划。可以每天准备一个话题，话题的内容最好是热门话题或常考话题。常见口语话题总结如下：Laid-off worker's problem、Reforms of housing policy 、Going abroad 、Globalization 、Information age、Environmental protection and economic development 、Online learning 、2008 Olympic, Beijing、Economic crisis 。热点话题在报纸、杂志上大多可以找到，也是很多考试写作部分常出的题目，因此也可以参照考研或四、六级作文范文。但切忌全篇背诵所找到的材料，最好只借用其中某些素材，然后用自己的语言重新整理。 3. 熟悉考场情况与考试流程 (1)与小组组员的交流(二对二考试模式) 小组成员可先模拟一下考试过程。让自己进入状态，而后可谈一些其他话题，放松一下。 (2)进入考场 入室前要敲门，虽是小节，但关系到你给考官的第一印象。 衣着得体，落落大方。 向考官问候：Good morning/ afternoon. 如果可以，微笑，但绝不可勉强。 (3)自我介绍 要求简洁、有新意，能够让考官记住你。最重要的是，发音要准，不要太快，以别人听懂为目的。但注意一定要听考官的指示语，听到考
SCI收录材料期刊影响因子及排名（一） Nature 自然 31.434 Science 科学28.103 Nature Material 自然（材料）23.132 Nature Nanotechnology 自然（纳米技术）20.571 Progress in Materials Science 材料科学进展18.132 Nature Physics 自然（物理）16.821 Progress in Polymer Science 聚合物科学进展16.819 Surface Science Reports 表面科学报告12.808 Materials Science & Engineering R-reports 材料科学与工程报告12.619 Angewandte Chemie-International Edition 应用化学国际版10.879 Nano Letters 纳米快报10.371 Advanced Materials 先进材料8.191 Journal of the American Chemical Society 美国化学会志8.091 Annual Review of Materials Research 材料研究年度评论7.947 Physical Review Letters 物理评论快报7.180 Advanced Functional Materials 先进功能材料 6.808 Advances in Polymer Science 聚合物科学发展 6.802 Biomaterials 生物材料 6.646 Small 微观？ 6.525 Progress in Surface Science 表面科学进展 5.429 Chemical Communications 化学通信 5.34 MRS Bulletin 材料研究学会（美国）公 告 5.290 Chemistry of Materials 材料化学 5.046 Advances in Catalysis 先进催化 4.812 Journal of Materials Chemistry 材料化学杂志 4.646 Carbon 碳 4.373 Crystal Growth & Design 晶体生长与设计 4.215 Electrochemistry Communications 电化学通讯 4.194 The Journal of Physical Chemistry B 物理化学杂志，B辑：材 料、表面、界面与生物物 理 4.189 Inorganic Chemistry 有机化学 4.147 Langmuir 朗缪尔 4.097 Physical Chemistry Chemical Physics 物理化学 4.064 International Journal of Plasticity 塑性国际杂志 3.875 Acta Materialia 材料学报 3.729 Applied Physics Letters 应用物理快报 3.726 Journal of power sources 电源技术 3.477
计算机英语口语对话实用表达 导读：我根据大家的需要整理了一份关于《计算机英语口语对话实用表达》的内容，具体内容：想要学好计算机英语需要大家掌握一些常用的计算英语口语，下面我为你带来计算机英语口语对话表达，供大家备考学习!计算机英语口语对话(一)A:Computers are ... 想要学好计算机英语需要大家掌握一些常用的计算英语口语，下面我为你带来计算机英语口语对话表达，供大家备考学习! 计算机英语口语对话(一) A:Computers are really spreading quickly, I just found the web site of the high school Iattended. 电脑发展得可真快。最近我发现了以前念的那所高中的网站。 、 B:Lots of schools have their own web sites. 很多学校都有自己的网站了。 A:Thats true, but when I was in high school, we just had a few computers, and now it looks likethe whole school is computerized. 是啊，以前念高中时学校只有寥寥几台电脑，现在好象整个学校都电脑化了。 计算机英语口语对话(二) A: So, tell me again what is this new job youre taking? 再告诉我一次，你现在的新工作是什么?
B:Ill be doing web design. · 我在做网页设计。 A:Web design?That sounds like work for a spider? 网页设计?听起来好象在替蜘蛛工作。 B:Im talking about designing pages for the World Wide Web; the Internet.我说的是替国际网络万维网设计网页。 计算机英语口语对话(三) A:Why does a company need a web site? 为何公司需要网站? ~ B:Not all companies need a web site, but it can be very helful in lots of ways. 不是每家公司都需要网站，不过在很多方面倒是很有帮助的。 For instance , many people search the web when they are looking for a place to buy something. 譬如说，有很多人想买东西时就会上网搜索， and if your company has a good web site ,you are much more likely to get that customersbusiness. 如果你的公司有个不错的网站，生意就很可能做起来了。 计算机英语口语对话(四) A:I dont understand why this E-mail keeps getting returned to me. …
SCI收录期刊影响因子排名表 Environmental Sciences & Engineering 044 Ecology Ranking Journal Title Impact Factor 1TRENDS IN ECOLOGY & EVOLUTION 6.678 2ECOLOGICAL MONOGRAPHS 5.300 3ANNUAL REVIEW OF ECOLOGY AND SYSTEMATICS 3.900 4ECOLOGY 3.139 5MOLECULAR ECOLOGY 3.086 6AMERICAN NATURALIST 2.903 7JOURNAL OF ECOLOGY 2.837 8JOURNAL OF ANIMAL ECOLOGY 2.801 9EVOLUTION 2.715 10BEHAVIORAL ECOLOGY AND SOCIOBIOLOGY 2.327 11ECOLOGICAL APPLICATIONS 2.180 12WILDLIFE MONOGRAPHS 2.000 13MARINE ECOLOGY-PROGRESS SERIES 1.923 14JOURNAL OF EVOLUTIONARY BIOLOGY 1.904 15OIKOS 1.860 16OECOLOGIA 1.854 17CONSERVATION BIOLOGY 1.832 18FUNCTIONAL ECOLOGY 1.818 19THEORETICAL POPULATION BIOLOGY 1.703 20TREE PHYSIOLOGY 1.640 21MICROBIAL ECOLOGY 1.606 22AQUATIC MICROBIAL ECOLOGY 1.474 23JOURNAL OF VEGETATION SCIENCE 1.414 24POLAR BIOLOGY 1.363