Distribution of spatial requirement for a MAP/G/1 queue when space and service times are dependent

Distribution of spatial requirement for a MAP/G/1 queue when space and service times are dependent

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Article ID: iaor19993182
Country: United States
Volume: 22
Issue: 1/2
Start Page Number: 121
End Page Number: 127
Publication Date: May 1996
Journal: Queueing Systems
Authors: ,
Keywords: MAP/G/1 queues, buffer allocation
Abstract:

In this paper, we consider a MAP/G/1 queue in which each customer arrives with a service and a space requirement, which could be dependent. However, the space and service requirements of different customers are assumed to be independent. Each customer occupies its space requirement in a buffer until it has completely received its service, at which time it relinquishes the space it occupied. We study and solve the problem of finding the steady-state distribution of the total space requirement of all customers present in the system. In the process of doing so, we also generalize the solution of the MAP/G/1 queue and find the time-average joint distribution of the queue-length, the state of the arrival process and the elapsed service time, conditioned on the server being busy. This problem has applications to the design of buffer requirements for a computer or communication system.

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