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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Sengupta, B., Takine, T. Distribution of spatial requirements for a MAP/G/1 queue when space and service times are dependent. Queueing Syst 22, 121–127 (1996). https://doi.org/10.1007/BF01159396
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DOI: https://doi.org/10.1007/BF01159396