Approximate Model for a Merge Configuration of Multiservers With Finite Capacity Intermediate Buffers

Abstract

We consider a queueing network consisting of multiservers in parallel and connected to a merger queue. All servers have an infinite capacity buffers. The configuration is decomposed into two subsystems: merging multi-servers and merger server and then analyzed in isolation. All times are assumed to be exponentially distributed. First we set and solve the equations for the aggregated merger queue, then express the occupancy probabilities of the original queue through the probabilities of the aggregated one, which reduces significantly the number of equations describing the behavior of the network. Using the fore-mentioned result, we derive expressions for the occupancy probabilities and other parameters of the merging queue.