Analysis of a queue with general service demands and correlated service capacities

Muynck, Michiel De; Bruneel, Herwig; Wittevrongel, Sabine

doi:10.1007/s10479-019-03396-8

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…general, i.i.d. full delay distribution De Muynck et al [15] correlated general, i.i.d. full delay distribution…”

Section: Servers Arrivals Delay Resultsmentioning

confidence: 99%

“…In [14], a continuous-time queueing system is treated where N servers are subject to breakdowns and repair; the results are the distributions of the queue length and waiting times. The authors of [15] obtain the queue length distribution and the delay distribution for a discrete-time model with general service demands and correlated service capacities. In their model, the service time of a customer depends on both its service demand and the service capacity.…”

Section: Introductionmentioning

confidence: 99%

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Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

2021

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In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number of arrivals and the number of available servers in a slot. Within a state, these numbers are independent and identically distributed random variables. State changes can only occur at slot boundaries and mark the beginnings and ends of state periods. Each state has its own distribution for its period lengths, expressed in the number of slots. The stochastic process that describes the state changes introduces correlation to the system, e.g., long periods with low arrival intensity can be alternated by short periods with high arrival intensity. Using probability generating functions and the theory of the dominant singularity, we find the tail probabilities of the delay.

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“…general, i.i.d. full delay distribution De Muynck et al [15] correlated general, i.i.d. full delay distribution…”

Section: Servers Arrivals Delay Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%