Computational methods and applications in queueing theory
Ann Oper Res
Computational methods and applications in queueing theory
Onno Boxma 0 1
Joris Walraevens 0 1
0 Department of Telecommunications and Information Processing, Ghent University , Ghent , Belgium
1 Department of Mathematics and Computer Science, Eindhoven University of Technology , Eindhoven , The Netherlands
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This issue of the Annals of Operations Research is devoted to papers from the first European
Conference on Queueing Theory (ECQT), which took place in Ghent, Belgium, August 20–
22, 2014. It continued a tradition started by the late Jesus Artalejo, who three times organized
a Madrid Conference on Queueing Theory. ECQT featured about 80 presentations. The
presenters of studies concerning computational methods and/or applications were offered
the opportunity to submit a paper based on their presented work to Annals of Operations
Research. The ten papers in this special issue have been chosen for publication after a careful
refereeing process. We would like to take this opportunity to express our gratitude to
Editorin-Chief Endre Boros, to Publications Manager Katie D’Agosta, and to the Springer staff
for their advice, support, and help. We are also indebted to the TPC of ECQT for their aid
in the review process and to the anonymous referees for their efforts. Below we give a brief
overview of the accepted papers.
De Muynck, Wittevrongel, and Bruneel study a discrete-time queueing system where
service capacities and service demands are explicitly modeled instead of being integrated
in the traditional concept of service times. Both are modeled by means of i.i.d. random
variables with general distributions. They derive (tail) distributions and moments for system
occupancy and waiting time in this non-standard model. Rumyantsev and Morozov also
study a queueing system with complications in the service times process. They model
highperformance clusters by means of multiserver systems in which each customer requires a
random number of servers simultaneously for a random amount of time. Stability criteria of
such a system under exponential assumptions and with an arbitrary number of servers are
obtained using a matrix-analytic approach. Another telecommunication application is studied
by Kim and Hwang. They analyze the relation between delay performance and the selection
distribution of the renewal access protocol, a simplified version of the IEEE 802.11 DCF
protocol. With the help of effective bandwidth theory, they derive conditions for the selection
distribution to optimize the queue overflow probability. However, they also show that it has
slow convergence to steady state compared with that of a Poisson selection distribution.
Besides communication and computer networks, call centers and risk management are still
hot application domains for queueing theory. Chen and Worthington study call centers with
time-dependent arrivals requiring time-dependent staffing levels. They evaluate an analytical
queueing model combined with an iterative staffing algorithm to be used for setting staffing
levels to achieve time-stable performance in call center type queues. Results show that the
method is faster than simulations while it is more accurate than standard analytical methods.
Yazici and Akar present a new numerical method to obtain ruin probabilities for a general
continuous-time risk problem with claims arriving according to a Markovian Arrival Process,
phase-type claim sizes, and multi-threshold premiums. By means of a sample path technique,
it is shown that the steady-state solution reduces to that of a certain multi-regime Markov
fluid queue. Tschaikowski and Tribastone prove convergence of steady-state open queueing
networks with many-server stations and Coxian-distributed service and abandonment times
to a fluid limit. The fact that their coupled ordinary differential equations are piecewise affine
enables a computational method for establishing the presence of a global attractor, based on
the solution of a system of linear matrix inequalities.
Two papers in this special issue discuss new aspects of some traditional queueing models.
Kim and Kim study a two-class priority M/G/1 retrial queueing system. Arriving high-priority
customers queue in a regular infinite-capacity queue, while low-priority customers have to
retry from a retrial orbit if the server is unavailable. Waiting time moments and distributions of
both types of customers are analyzed. Chaudhry, Banik, and Pacheco analyze a batch arrival
single-server queue with generally distributed batch interarrival times, generally distributed
batch sizes, and a Markovian service process. The analysis is based on roots of the associated
characteristic equation of the vector-generating function of system-length distribution at an
arrival instant. They also establish heavy- and light-traffic approximations.
Finally, the last two papers concern the output and loss process respectively. Steyaert,
Wittevrongel, and Bruneel characterize the output (...truncated)