Superposition of renewal processes and an application to multi-server queues

• Published in: Statistics & probability letters Vol. 76; no. 17; pp. 1914 - 1924
• Main Authors: Kella, Offer, Stadje, Wolfgang
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2006; Elsevier
• Series: Statistics & Probability Letters
• Subjects: Exact sciences and technology; Forward recurrence times; Joint distribution; Mathematics; Multi-server queue; Probability and statistics; Probability theory and stochastic processes; Renewal processes; Renewal processes Superposition Forward recurrence times Joint distribution Multi-server queue; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Superposition; secondary; Primary; Forward recurrence times; Renewal processes; Superposition; Joint distribution; Multi-server queue; Recurrence relation; Probability theory; Renewal process; Waiting time; Renewal processes; Superposition; Forward recurrence times; Joint distribution; Multi-server queue; Multiserver queue; Point process; Arrival process; Distribution function; Forward recurrence time; Primary 60K05; secondary 60K25; Queue
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/j.spl.2006.04.041

The aim of this paper is to compare the waiting times of customers in multiple-server queues, where the idle times are removed, with different numbers of servers. For this purpose we develop some results regarding the vector-valued marked point process whose points are arrival epochs of the superposition of renewal processes with different continuous inter-arrival distribution and the marks are the vectors of forward recurrence times of the various renewal processes at these arrival epochs.