Queues of Queues in Communication Networks

Citation

Hernández Valencia, Enrique José (1988) Queues of Queues in Communication Networks. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/wygw-0f83. https://resolver.caltech.edu/CaltechETD:etd-11072007-090157

Abstract

The concept of a camp-on queueing system is related to the idea of having systems of multiple hierarchical queues. Customers requesting service at a service center are queued at one of different queueing stages based on the location of the customer's intended server within the service hierarchy. In many instances, customers in a camp-on model exhibit a dual function customer-server, giving rise to a system with queues of queues. For this model, we assume Poisson distributed arrivals with different classes of customers for each queueing level. The service completion process is regarded as exponentially distributed, a standard assumption for many communication systems.

Here we discuss a stationary model for such a Markovian camp-on system. Closed-form solutions are derived for various state occupancy distributions of interest (e.g., joint probability distribution of queue lengths, marginal distributions for subsystems, accumulated workload, etc.), in systems with finite and infinite storage capacity and two queueing levels. Most of these results are also extended to multilevel queueing systems. It is found that this camp-on model is stable whenever all the distinct queues, in isolation, behave as stable systems. The form of the joint probability distribution of queue lengths is not a product of the independent contributions from each subsystem, since it must also account for the relative position of the queues with respect to the initial service center, the root of the service hierarchy.

Two particular applications are discussed in detail: 1) PBX-like communication services, and 2) broadcast delivery services. Performance statistics such as waiting time distributions, blocking probabilities and mean response time are derived. These results show that we do not pay too large a penalty for introducing two or more levels of queueing, and under very extreme conditions (heavy traffic) the delay in response increases only linearly with the number of queueing stages. Broadcast service strategies provide even better performance than conventional point-to-point service, though a broadcast medium is required.

Thesis Files