A Finite Capacity Queuing Network with Single and Multiple Processing Nodes
R. O. Onvural and I. F. Akyildiz
Queueing Networks with Finite Capacity
We consider a queuing network consisting of two nodes connected in series. Jobs (or customers) arrive at node I according to a Poisson process of rate λ. There is a finite buffer in front of node 1 and any arrival that finds the buffer full is considered lost. Jobs are processed one at a time in node 1 by a single server and proceed to node 2, where they are served in groups of varying size by another server. A dynamic service rule in terms of a pre- specified number is used at node 2, which also has a finite buffer. The service times of the jobs in both nodes are assumed to be independent and exponentially distributed with (possibly) different parameters. We study this queuing network using Markov process by obtaining expressions for the steady-state queue length densities at arbitrary time points and at departures, which are the main ingredients for computing various system performance measures such as the throughput, fraction of time the server in node 1 is blocked, fraction of time the servers are idle and the fraction of lost jobs. Efficient algorithmic procedures for computing the steady-state queue length densities and other system performance measures are discussed. Some numerical examples are presented.
© 1993 Published by Elsevier Ltd.
Chakravarthy, Srinivas R., "A Finite Capacity Queuing Network with Single and Multiple Processing Nodes" (1993). Industrial & Manufacturing Engineering Publications. 90.