A. B. Clarke's Tandem Queue Revisited—Sojourn Times

Abstract

In telecommunications, packets or units may complete their service in a different order from the one in which they enter the station. In order to reestablish the original order resequencing protocols need to be implemented. In this article, the focus is on a two-server resequencing system with heterogeneous servers and two buffers. One buffer has an infinite capacity to hold the incoming units. The other with a finite capacity is used to resequence the serviced units. This is to maintain the order of departure of the units according to the order of their arrivals. To analyze this resequencing model, we introduce an equivalent two-stage queueing system, namely A. B. Clarke's Tandem Queue, in which the arriving units receive service from only one server, and the units departing from the first stage may be temporally prevented from leaving by occupied service units at the second stage. Our interest is to study the resequencing delay and the sojourn time as times until absorption in suitably defined quasi-birth-and-death processes and continuous-time Markov chains.

Keywords:

• Blocking
• Resequencing
• Sojourn times
• Queueing

Mathematics Subject Classification:

• Primary 60K25
• Secondary 68M20, 90B22