Note that this allows for dynamic changes in the service
rates, as well as in the demand rates.
Extending the work of Koopman (1972), the
Mt/Ekt/k system was proposed by Kivestu (1976)
as a model that could be used to directly compute
approximate queueing statistics for airports—
rather than separately solving the M(t)/M(t)/k and
M(t)/D(t)/k models and then somehow interpolating
their results. (Note that negative exponential service
times (M and constant service times (D) are simply
special cases of the Erlang (Ek) family, with k = 1
and k=, respectively.) Kivestu (1976) noted that k
should be determined from the relationship ES
/S
√ =
k, where ES
and S denote the expected value
and the standard deviation of the service times and
can be estimated from field data. He also developed
a powerful numerical approximation scheme
that computes the (time varying) state probabilities
for the Mt/Ekt/k system efficiently. Malone (1995)
has demonstrated the accuracy and practicality of
Kivestu’s (1976) approach and developed additional
efficient approximation methods, well suited to the
analysis of dynamic airfield queues. Fan and Odoni
(2002) provide a description of the application of
Kivestu’s (1976) model to a study of the gridlock conditions
that prevailed at LaGuardia Airport in 2000
and early 2001.
Additional (numerical) analytical models for computing
airport delays have been developed over the
last few years. Peterson et al. (1995) and Daniel
(1995) describe two different models for computing
delays at hub airports, which are characterized by
sharp “banks” or “waves” of arrivals and departures.
Hansen (2002) has used a deterministic model, based
on the notion of cumulative diagrams, to compute
delay externalities at Los Angeles International Airport.
Finally, Long et al. (1999) and Malone (1995)
present two dynamic queueing network models and
their application to the study of congestion in the
National Airspace System. Ingolfsson et al. (2002)
offer a comprehensive survey and comparison of several
alternative approaches to the analysis of nonstationary
queueing systems.
Many of the best features of some of the analytical
capacity and delay models just described have
been integrated recently in a number of new software
Transportation Science/Vol. 37, No. 4, November 2003 383
Downloaded from
Note that this allows for dynamic changes in the servicerates, as well as in the demand rates.Extending the work of Koopman (1972), theMt/Ekt/k system was proposed by Kivestu (1976)as a model that could be used to directly computeapproximate queueing statistics for airports—rather than separately solving the M(t)/M(t)/k andM(t)/D(t)/k models and then somehow interpolatingtheir results. (Note that negative exponential servicetimes (M and constant service times (D) are simplyspecial cases of the Erlang (Ek) family, with k = 1and k=, respectively.) Kivestu (1976) noted that kshould be determined from the relationship E S/S√ =k, where E S and S denote the expected valueand the standard deviation of the service times andcan be estimated from field data. He also developeda powerful numerical approximation schemethat computes the (time varying) state probabilitiesfor the Mt/Ekt/k system efficiently. Malone (1995)has demonstrated the accuracy and practicality ofKivestu’s (1976) approach and developed additionalefficient approximation methods, well suited to theanalysis of dynamic airfield queues. Fan and Odoni(2002) provide a description of the application ofKivestu’s (1976) model to a study of the gridlock conditionsthat prevailed at LaGuardia Airport in 2000and early 2001.Additional (numerical) analytical models for computingairport delays have been developed over thelast few years. Peterson et al. (1995) and Daniel(1995) describe two different models for computingdelays at hub airports, which are characterized bysharp “banks” or “waves” of arrivals and departures.Hansen (2002) has used a deterministic model, basedon the notion of cumulative diagrams, to computedelay externalities at Los Angeles International Airport.Finally, Long et al. (1999) and Malone (1995)present two dynamic queueing network models andtheir application to the study of congestion in theNational Airspace System. Ingolfsson et al. (2002)offer a comprehensive survey and comparison of severalalternative approaches to the analysis of nonstationaryqueueing systems.Many of the best features of some of the analyticalcapacity and delay models just described havebeen integrated recently in a number of new softwareTransportation Science/Vol. 37, No. 4, November 2003 383Downloaded from
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