Stationary Characteristics Of Homogenous Geo/Geo/2 Queue With Resequencing In Discrete Time

Abstract

Resequencing problem is a crucial issue in communication systems, databases, production and information networks because correct processing of information by them may often be performed only if original order of packets, queries, jobs is preserved. In this paper consideration is given to one of the queueing systems that may model processes of discrete nature where resequencing phenomenon may arise. Specifically Geo/Geo/2/∞ queueing system with reordering buffer of infinite capacity is being analyzed. Expressions for stationary sojourn time distribution and joint stationary distribution of the number of customers in system and reordering buffer are given in explicit form and in terms of generating functions. Illustrative numerical example is presented.

Joint Stationary Distribution Of Queues In Homogenous M|M|3 Queue With Resequencing

“…Following this approach various problems setting have been considered and solved including distribution of number of packets in reordering buffer and in system under different assumptions about arrival and service process (see, e.g. Jain and Sharma (2011), , Chakravarthy (1998), Takine et al (1994), De Nicola C. et al (2013)); distribution and/or mean of the resequencing delay (see, e.g. Huisman and Boucherie (2002), Ding et al (1991)), end-to-end (i.e.…”