A Study of the Queueing Systems M/G/1 and GI/M/1, Softcover reprint of the original 1st ed. 1968
Lecture Notes in Economics and Mathematical Systems Series, Vol. 2

This study has grown out of a part of the author's thesis "Some Simple and Bulk Queueing Systems: A Study of Their Transient Behavior" submitted to the University of Western Australia (1964) and a course on Queueing Theory given to graduate students in the Operations Research Group of Case Institute of Technology, Cleveland, Ohio. The one semester course (approximately 35 hours) consisted of the following topics. (i) Some of the important special queues such as M/M/s, M/D/s, M/Ek/l etc., with emphasis on the different methods employed in the transient as well as steady state solution. (ii) Imbedded Markov chain analysis of M/G/l and GI/M/l as given in the joint paper of the author and N. U. Prabhu as well as the papers of D. G. Kendall. [All notations and papers are referred to later in the notes]. (iii) The contents of this memorandum. The author feels that such a course prepares the students adequately for an advanced course in Queueing Theory involving topics on Waiting Times, the General Queue GI/G/l and other ramifications such as Priorities, etc. A few words regarding the approach adopted in this study may not be out of place. So far, the time dependent behavior of queueing systems has not found a place in courses given outside the Department of Mathematics.

1. The Queue M/G/1 with Group Arrivals.- 1.1 Description and Definitions.- 1.2 Busy Period Transitions.- 1.3 General Transitions of Q(T).- 1.4 Limiting Behavior of Q(T).- 1.5 Q(T) and the Unexpended Service Time.- 1.6 Waiting Time W(T): An Approach Through Q(T).- 1.7 Waiting Time W(T): An Independent Study.- 1.8 The Queue M/G/L with Balking.- 1.9 Special Cases.- 2. The Queue GI/M/1 with Group Service.- 2.1 Description and Definitions.- 2.2 The Busy Period T0.- 2.3 The Busy Period T1.- 2.4 The Busy Cycle.- 2.5 General Transitions of Q(T).- 2.6 Waiting Time W(T).- 3. Queueing Systems in Discrete Time.- 3.1 The Queue Geom/G/1.- 3.2 The Queue Gi/Geom/1.