Rejoinder on: Queueing models for the analysis of communication systems

Abstract

First of all, we want to express our gratitude to the former Editor-in-Chief of the journal TOP, our fondly-remembered colleague Professor Jesús Artalejo, who invited us about one year ago to write a review paper for TOP on the topic of queueing models for the analysis of communication systems. Also, we want to thank the three discussants for the effort of carefully reading our paper and adding interesting information. We mention in particular the insightful discussion of Onno Boxma on the role of transform methods in queueing analysis, their strengths and weaknesses. With respect to scheduling disciplines, Onno Boxma also adds the topic of dynamic priority scheduling schemes. As far as traffic modeling is concerned, Alexander Dudin not only refers to the well-known D-BMAP model as an alternative description of bursty, correlated traffic streams, but he also points to several related papers on continuous-time models with session-based arrivals. Harry Perros emphasizes the practical applications of discrete-time queueing models in the performance evaluation of various subsystems of modern telecommunication networks. In particular, he discusses the restriction introduced by the assumption in our paper that packets be of fixed length, which makes the results applicable in the context of ATM, in optical burst switching, and in HTTP adaptive video streaming, but not in a general IP network where packets typically are of variable length.A very striking observation is that all three discussants explicitly comment on the use of discrete-time queueing models in much of our work of the last thirty years (including the current paper), as opposed to the much more frequently encountered continuous-time models in literature. As these remarks are of a very generic nature, we isolate this topic from the more specific comments in this rejoinder. Therefore, our responses are structured around two main topics: (1) the aspect of modeling and queueing analysis in the discrete time domain and (2) possible extensions of and remarks on our presented analysis of the two-class priority queue with train arrivals. * SMACS: Stochastic Modeling and Analysis of Communication Systems