Two parallel finite queues with simultaneous services and Markovian arrivals

[摘要] In this paper, we consider a finite capacity single server queueing model with two buffers,AandB, of sizesKandNrespectively. Messages arrive one at a time according to a Markovian arrival process. Messages that arrive at bufferAare of a different type from the messages that arrive at bufferB. Messages are processed according to the following rules: 1. When bufferA(B)has a message and bufferB(A)is empty, then one message fromA(B)is processed by the server. 2. When both buffers,AandB, have messages, then two messages, one fromAand one fromB, are processed simultaneously by the server. The service times are assumed to be exponentially distributed with parameters that may depend on the type of service. This queueing model is studied as a Markov process with a large state space and efficient algorithmic procedures for computing various system performance measures are given. Some numerical examples are discussed.

[学科分类] 应用数学