This thesis has to do with certain fundamental queues that are well established as models for delay in simple packet-switching concentrators and networks. We first revisit the single server queue with Poisson arrivals and general independent service times. We then work out a complete delay analysis for a traffic concentrating tandem network of queues with deterministic service and batch Poisson sources connected to every node; this is the most comprehensive analysis available for a network which is not of Jackson type. We also show how to (partially) extend the analysis to a concentrating tree network, and to an arrival process somewhat more general that batch Poisson. / The two parts of the thesis have a close methodological relationship. Our contribution in both cases is to rederive certain known results, and to produce a variety of new ones, using techniques that are essentially qualitative. Our particular view of the stochastic processes in question is guided by a very special queue discipline, namely Last Come First Served preemptive resume; by identifying certain structural features of the sample paths, one can read, almost without calculation, a host of statistics of common interest. The LCFS preemptive resume discipline also enables us: (i) to strengthen the connection between the single server queue with general independent service times and interarrival times, and the fluctuation theory of random walks; (ii) to strengthen the connection between the queue with Poisson arrivals and branching processes.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.71999 |
| Date | January 1985 |
| Creators | Shalmon, Michael S. |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Electrical Engineering.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000219546, proquestno: AAINL20863, Theses scanned by UMI/ProQuest. |
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