DISTRIBUTION OF SPATIAL REQUIREMENTS FOR A MAP G/1 QUEUE WHEN SPACE AND SERVICE TIMES ARE DEPENDENT/

In this paper, we consider a MAP/G/1 queue in which each customer arri ves 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 requireme nt in a buffer until it has completely received its service, at which time, it relinquishes the space it occupied. We study and solve the pr oblem of finding the steady-state distribution of the total space requ irement of all customers present in the system. In the process of doin g so, we also generalize the solution of the MAP/G/1 queue and find th e time-average joint distribution of the queue-length, the state of th e arrival process and the elapsed service time, conditioned on the ser ver being busy. This problem has applications to the design of buffer requirements for a computer or communication system.