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: | Sengupta Bhaskar, Takine Tetsuya |
Keywords: | MAP/G/1 queues, buffer allocation |
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.