TY - JOUR

T1 - Large deviations of an infinite-server system with a linearly scaled background process

AU - De Turck, K.E.E.S.

AU - Mandjes, M.R.H.

PY - 2014

Y1 - 2014

N2 - This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates ¿i¿i by a factor NN and the transition rates ¿ij¿ij of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where NN tends to 88). The paper also presents qualitative properties of the system’s behavior conditional on the rare event under consideration happening.
Keywords: Queues; Infinite-server systems; Markov modulation; Large deviations

AB - This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates ¿i¿i by a factor NN and the transition rates ¿ij¿ij of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where NN tends to 88). The paper also presents qualitative properties of the system’s behavior conditional on the rare event under consideration happening.
Keywords: Queues; Infinite-server systems; Markov modulation; Large deviations

U2 - 10.1016/j.peva.2014.01.001

DO - 10.1016/j.peva.2014.01.001

M3 - Article

SN - 0166-5316

VL - 75-76

SP - 36

EP - 49

JO - Performance Evaluation

JF - Performance Evaluation

ER -