The M/M/1 queue with randomly varying arrival and service rates: A phase substitution solution

The M/M/1 queue with randomly varying arrival and service rates: A phase substitution solution

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Article ID: iaor1989343
Country: United States
Volume: 35
Issue: 5
Start Page Number: 561
End Page Number: 570
Publication Date: May 1989
Journal: Management Science
Authors: ,
Keywords: computational analysis, markov processes
Abstract:

This paper presents an alternative procedure for computing the steady state probability vector of an M/M/1 queue with randomly varying arrival and service rates. By exploiting the structure of the infinitesimal generator of the underlying continuous-time Markov chain, the approach represents an efficient adaptation of the state reduction method introduced by Grassmann for solving problems involving M/M/1 queues under a random environment. The authors compare computational requirements of the proposed approach with the method of Neuts and block elimination under different rush-hour congestion patterns while keeping the overall traffic intensity constant as well as under different traffic intensities. They demonstrate that the proposed method requires minimal computing time to reach convergence and moreover the time requirement does not change much when traffic intensity increases.

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