Queuing with Heterogeneous Users: Block Probability and Sojourn times

TL;DR

This paper analyzes a two-class queueing system with impatient and tolerant users, characterizing the achievable performance region, proposing a pseudo conservation law, and demonstrating the benefits of dynamic resource sharing policies.

Contribution

It introduces the achievable region for heterogeneous queueing with static policies, proposes a pseudo conservation law, and compares static and dynamic policies for resource sharing.

Findings

Achievable region characterized for static policies.

Pseudo conservation law relating blocking probability and sojourn time.

Dynamic policies expand the achievable performance region.

Abstract

Communication networks need to support voice and data calls simultaneously. This results in a queueing system with heterogeneous agents. One class of agents demand immediate service, would leave the system if not provided. The second class of customers have longer job requirements and can wait for their turn. We discuss the achievable region of such a two class system, which is the region of all possible pairs of performance metrics. Blocking probability is the relevant performance for eager/impatient class while the expected sojourn time is appropriate for the second tolerant class. We obtain the achievable region, considering static policies that do not depend upon the state of the second class. We conjecture a pseudo conservation law, in a fluid limit for eager customers, which relates the blocking probability of eager customers with the expected sojourn time of the tolerant customers. Using this conjecture we obtain the static achievable region. We validate the pseudo conservation law using two example families of static schedulers, both of which achieve all the points on the achievable region. Along the way we obtain smooth control (sharing) of resources between voice and data calls. We also consider an example dynamic policy to establish that the dynamic achievable region is strictly bigger than the static region, for this heterogeneous queueing system.