dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Morozov, Evsey |
dc.date.accessioned |
2008-09-04T14:13:31Z |
dc.date.available |
2008-09-04T14:13:31Z |
dc.date.created |
2007-12 |
dc.date.issued |
2007-12 |
dc.identifier.uri |
http://hdl.handle.net/2072/9171 |
dc.format.extent |
29 |
dc.format.extent |
247290 bytes |
dc.format.mimetype |
application/pdf |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;779 |
dc.rights |
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
dc.subject.other |
Cues, Teoria de |
dc.title |
Coupling and monotonicity of queueing processes |
dc.type |
info:eu-repo/semantics/preprint |
dc.subject.udc |
51 - Matemàtiques |
dc.description.abstract |
The main purpose of this work is to give a survey of main monotonicity properties of queueing processes based on the coupling
method. The literature on this topic is quite extensive, and we do not consider all aspects of this topic. Our more concrete goal is to
select the most interesting basic monotonicity results and give simple and elegant proofs. Also we give a few new (or revised) proofs of a few important monotonicity properties for the queue-size and workload processes both in single-server and multi- server systems.
The paper is organized as follows. In Section 1, the basic notions and results on coupling method are given. Section 2 contains known
coupling results for renewal processes with focus on construction of synchronized renewal instants for a superposition of independent renewal processes. In Section 3, we present basic monotonicity results for the queue-size and workload processes. We consider both discrete-and continuous-time queueing systems with single and multi servers.
Less known results on monotonicity of queueing processes with dependent service times and interarrival times are also presented. Section 4 is devoted to monotonicity of general Jackson-type queueing networks with Markovian routing. This section is based on the notable paper [17]. Finally, Section 5 contains elements of stability analysis of regenerative queues and networks, where coupling and monotonicity results play a crucial role to establish minimal suficient stability conditions. Besides, we present some new monotonicity results for tandem networks. |