On the Nonsymmetric Longer Queue Model : Joint Distribution, Asymptotic Properties, and Heavy Traffic Limits

Abstract EN

We consider two parallel queues, each with independent Poisson arrival rates, that are tended by a single server.

The exponential server devotes all of its capacity to the longer of the queues.

If both queues are of equal length, the server devotes ν of its capacity to the first queue and the remaining 1−ν to the second.

We obtain exact integral representations for the joint probability distribution of the number of customers in this two-node network.

Then we evaluate this distribution in various asymptotic limits, such as large numbers of customers in either/both of the queues, light traffic where arrivals are infrequent, and heavy traffic where the system is nearly unstable.