Analysis of the loss probability in the M/G/1+G queue

We consider the loss probability in the stationary M/G/1+G queue, i.e., the stationary M/G/1 queue with impatient customers whose impatience times are generally distributed. It is known that the loss probability is given in terms of the probability density function v ( x ) of the virtual waiting tim...

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Bibliographic Details
Published in:Queueing systems 2015-08, Vol.80 (4), p.363-386
Main Authors: Inoue, Yoshiaki, Takine, Tetsuya
Format: Article
Language:English
Subjects:
Business and Management
Computer Communication Networks
Control
Customer services
Customers
Integral equations
Operations Research/Decision Theory
Probability density functions
Probability Theory and Stochastic Processes
Queues
Random variables
Supply Chain Management
Systems Theory
Volterra integral equations
Workloads
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Summary:We consider the loss probability in the stationary M/G/1+G queue, i.e., the stationary M/G/1 queue with impatient customers whose impatience times are generally distributed. It is known that the loss probability is given in terms of the probability density function v ( x ) of the virtual waiting time and that v ( x ) is given by a formal series solution of a Volterra integral equation. In this paper, we show that the series solution of v ( x ) can be interpreted as the probability density function of a random sum of dependent random variables and we reveal its dependency structure through the analysis of a last-come first-served, preemptive-resume M/G/1 queue with workload-dependent loss. Furthermore, based on this observation, we show some properties of the loss probability.
ISSN:0257-0130
1572-9443
DOI:10.1007/s11134-015-9449-7