Abstract
In the paper, we investigate one-server queueing system with stationary Poisson arrival process, non-homogeneous customers and unreliable server. As non-homogenity, we mean that each customer is characterized by some arbitrarily distributed random capacity that is called customer volume. Service time of a customer generally depends on his volume. The server can be broken when it is free or busy and the renewal period goes on for random time having an arbitrary distribution. During this period, customers present in the system and arriving to it are not served. Their service continues immediately after renewal period termination. For such systems, we determine the distribution of total volume of customers present in it. An analysis of some special cases and some numerical examples are attached as well.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aleksandrov, A.M., Katz, B.A.: Non-homogeneous demands arrival servicing. Izv. AN SSSR. Tekhnicheskaya Kibernetika. 2, 47–53 (1973). (in Russian)
Bocharov, P.P., D’Apice, C., Pechinkin, A.V., Salerno, S.: Queueing Theory. VSP, Utrecht-Boston (2004)
Gnedenko, B.V., Danielyan, E.A., Dimitrov, B.N., Klimov, G.P., Matveev, V.F.: Priority Queues. Moscow University Edition, Moscow (1973). (In Russian)
Klimov, G.P.: Stochastic Service System. Nauka, Moscow (1966). (In Russian)
König, D., Stoyan, D.: Methoden der Bedienungstheorie. Akademie-Verlag, Berlin (1976)
Sengupta, B.: The spatial requirements of M/G/1 queue or: how to design for buffer space. Lect. Notes Contr. Inf. Sci. 60, 547–562 (1984). https://doi.org/10.1007/BFb0005191
Tian, N., Zhang, Z.G.: Vacation Queueing Models Theory and Applications. ISORMS, vol. 93. Springer, Boston (2006). https://doi.org/10.1007/978-0-387-33723-4
Tikhonenko, O.M.: Determination of the characteristics of the total amount of customers in queues with absolute priority. Automation and Remote Control. vol. 60, part 2, no. 8, p. 1205–1210 (1999)
Tikhonenko, O.M.: Distribution of total message flow in single-server queueing system with group arrival. Autom. Remote Control 46(11), 1412–1416 (1985)
Tikhonenko, O.M.: The problem of determination of the summarized messages volume in queueing system and its applications. J. Inf. Process. Cybern. 32(7), 339–352 (1987)
Tikhonenko, O.M.: Distribution of total flow of calls in group arrival queueing systems. Autom. Remote Control 48(11), 1500–1507 (1987)
Tikhonenko, O.: Queueing Models in Computer Systems. Universitetskoe, Minsk (1990). (In Russian)
Tikhonenko, O.M.: Computer Systems Probability Analysis. Akademicka Oficyna Wydawnicza EXIT, Warsaw (2006). (In Polish)
Tikhonenko, O., Ziółkowski, M.: Single-server queueing system with external and internal customers. Bull. Polish Acad. Sci. Tech. Sci. 66(4), 539–551 (2018). https://doi.org/10.24425/124270
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Tikhonenko, O., Ziółkowski, M. (2020). Unreliable Single-Server Queueing System with Customers of Random Capacity. In: Gaj, P., Gumiński, W., Kwiecień, A. (eds) Computer Networks. CN 2020. Communications in Computer and Information Science, vol 1231. Springer, Cham. https://doi.org/10.1007/978-3-030-50719-0_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-50719-0_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-50718-3
Online ISBN: 978-3-030-50719-0
eBook Packages: Computer ScienceComputer Science (R0)