Analysis of multiserver retrial queueing system: A martingale approach and an algorithm of solution |
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Authors: | Vyacheslav M Abramov |
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Institution: | (1) School of Mathematical Sciences, Monash University, Building 28M, Clayton Campus, Clayton, VIC, 3800, Australia |
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Abstract: | The paper studies a multiserver retrial queueing system withm servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system
occupies one of the free servers. If upon arrival all servers are busy, then the customer goes to the secondary queue, orbit,
and after some random time retries more and more to occupy a server. A service time of each customer is exponentially distributed
random variable with parameter μ1. A time between retrials is exponentially distributed with parameter μ2 for each customer. Using a martingale approach the paper provides an analysis of this system. The paper establishes the stability
condition and studies a behavior of the limiting queue-length distributions as μ2 increases to infinity. As μ2→∞, the paper also proves the convergence of appropriate queue-length distributions to those of the associated “usual” multiserver
queueing system without retrials. An algorithm for numerical solution of the equations, associated with the limiting queue-length
distribution of retrial systems, is provided.
AMS 2000 Subject classifications: 60K25 60H30. |
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Keywords: | Multiserver retrial queues Queue-length distribution Stochastic calculus Martingales and semimartingales |
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