Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

This paper compares two discrete-time single-server queueing models with queues. In both models, the server is available to a queue probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for joint moments not feasible, we rely on heavy-traffic limit approach. The correlation coefficient of queue-contents computed via solution two-dimensional functional equation obtained by reducing it boundary value problem hyperbola. most server-sharing assumed that system work-conserving in sense if one queues empty, customer other served 1. our second model, omit this rule such can be idle case non-empty queue. Contrary what would expect, resulting approximations reveal remain different critically loaded