Methodol Comput Appl Probab (2017) 19:819–841
Perturbation Analysis of the GI/M/s Queue
· Karim Abbas
· Djamil A
Received: 5 August 2015 / Revised: 9 August 2016 /
Accepted: 11 September 2016 / Published online: 29 September 2016
© Springer Science+Business Media New York 2016
Abstract This paper investigates the M/M/s queueing model to predict an estimate for the
proximity of the performance measures of queues with arrival processes that are slightly
different from the Poisson process. Specifically, we use the strong stability method to obtain
perturbation bounds on the effect of perturbing the arrival process in the M/M/s queue.
Therefore, we build some algorithms based on strong stability method to predict stationary
performance measures of the GI/M/s queue. Some numerical examples are sketched out to
illustrate the accuracy of the proposed method.
Keywords Markov chains · Queueing system · Strong stability · Algorithm · Simulation
Mathematics Subject Classsification (2010) 68M20 · 60K25 · 60J10
Stationary performance indices of simple Markovian systems, such as the queue length
probabilities for the M/M/s queue, are analytic functions of the system’s parameters: the
service rate and the inter-arrival rate. This observation has initiated the study of analytical
properties of stochastic systems. As many other stochastic models, queueing systems can be
entirely described by Markov chains. There exists numerous results on perturbation bounds
of Markov chains. General results are summarized by Heidergott and Hordijk (2003).
LaMOS, University of Bejaia, Targua Ouzemour, Bejaia, 06000, Algeria