Publication: Generalized birth and death processes with applications to queues with repeated attempts and negative arrivals
Loading...
Full text at PDC
Publication Date
1998
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
We consider the stochastic behaviour of a Markovian bivariate process {(C(t), N(t)), t greater than or equal to 0} whose state-space is a semi-strip S = {0, 1} x N. The intensity matrix of the process is taken to get a limit distribution P-ij = lim(t-->+infinity) P{(C(t), N(t)) = (i, j)} such that {P-0j, j is an element of N}, or alternatively {P-lj, j is an element of N}, satisfies a system of equations of 'birth and death' type. We show that this process has applications to queues with repeated attempts and queues with negative arrivals. We carry out an extensive analysis of the queueing process, including classification of states, stationary analysis, waiting time, busy period and number of customers served.
Description
The authors are grateful to the referees for helpful comments. This research was supported by the DGICYT under grant PB95-0416.
UCM subjects
Unesco subjects
Keywords
Citation
Artalejo JR (1993) Explicit formulae for the characteristics of theM/H 2/1 retrial queue. J Oper Res Soc44, 309-313
Artalejo JR (1994) New results in retrial queueing systems with breakdown of the servers. Stat Neerl48, 23-36
Artalejo JR, Gomez-Corral A (1997) Steady state solution of a single-server queue with linear repeated requests. J Appl Probab34, 223-233
Asmussen S (1987) Applied Probability and Queues. Wiley, New York
Boucherie RJ, Boxma OJ (1995) The workload in the M/G/1 queue with work removal. Probab Engrg Inform Sci10, 261-277
Chao X (1995) A queueing network model with catastrophes and product form solution. Oper Res Letters18, 75-79
Chao X, Pinedo M (1995) Networks of queues with batch services, signals and product form solutions. Oper Res Letters17, 237-242
Choo QH, Conolly B (1979) New results in the theory of repeated orders queueing systems. J Appl Probab16, 631-640
Falin GI (1980) An M/M/1 queue with repeated calls in presence of persistence function. Paper 1606-80, All-Union Institute for Scientific and Technical Information, Moscow
Falin GI (1990) A survey of retrial queues. Queueing Syst7, 127-168
Falin GI, Fricker C (1991) On the virtual waiting time in anM/G/1 retrial queue. J Appl Probab28, 446-460
Farahmand K (1990) Single line queue with repeated demands. Queueing Syst6, 223-228
Fayolle G (1986) A simple telephone exchange with delayed feedbacks. In: Boxma OJ, Cohen JW, Tijms HC (eds) Teletraffic Analysis and Computer Performance Evaluation. Elsevier, Amsterdam
Gelenbe E (1991) Product-form queueing networks with negative and positive customers. J Appl Probab28, 656-663
Hanschke T (1987) Explicit formulas for the characteristics of theM/M/2/2 queue with repeated attempts. J Appl Probab24, 486-494
Harrison PG, Pitel E (1993) Sojourn times in single-server queues with negative customers. J Appl Probab30, 943-963
Harrison PG, Pitel E (1996) The M/G/1 queue with negative customers. Adv Appl Probab28, 540-566
Herdenson W, Northcote BS, Taylor PG (1994) Geometric equilibrium distributions for queues with interactive batch departures. Ann Oper Res48, 493-511
Jain G, Sigman K (1996) A Pollaczek-Khintchine formulation for M/G/1 queues with disasters. J Appl Probab33, 1191-1200
Martin M, Artalejo JR (1995) Analysis of anM/G/1 queue with two types of impatient units. Adv Appl Probab27, 840-861
Neuts MF (1981) Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The John Hopkins University Press
Yang T, Templeton JGC (1987) A survey on retrial queues. Queueing Syst2, 203-233