Model For A Merge Configuration of Identical Single Servers with Finite Capacity Buffers

Abstract

We consider a queuing network consisting of identical single servers in parallel and connected to a merger queue. All servers have finite capacity buffers of equal size. The configuration is decomposed into two subsystems: merging servers and merger server and then analyzed in isolation. All times of the merging servers are assumed to be exponentially and identically distributed, but the service time of the merger queue is quite generally distributed. First we set and solve integro-differential equations for the merger queue, then express the occupancy probabilities of the merging queue through the probabilities of the merger, which reduces significantly the number of equations describing the behavior of the network.