On One Model of Multichannel Queuing System with Unreliable Repairable Servers and Input Memory

Ramaz R. Shamugia

Research Department of Radiophysics and Electronic Systems Modeling, Ilia Vekua Sukhumi Institute of Physics and Technology, Tbilisi, Georgia.

DOI: 10.4236/ijcns.2014.78030                

Abstract

The work deals with the development of analytical model of multichannel technical queuing system with unreliable servers and input memory where server failure flows and incoming request flows comply with Poissonian laws, while the flows of failed facilities repairs and flows of incoming requests comply with exponential laws of probability distribution. Random process of system change-over is a Markovian process with continuous time and discrete states. Relations binding basic parameters and output characteristics of the system indicated are obtained as probabilities of system staying in the given moment in one of the possible states. The proposed model is the most generalized compared to some models known in literature which could be considered as special cases of the considered model.

Keywords

Multichannel Queuing Systems, QS with Unreliable Facilities, QS with Repairable Facilities, Servers with Failures, QS with Queues

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Gnedenko, B.V. and Kovalenko, I.N. (2012) Introduction to Queuing Theory. LKT, 400.
[2]	Saati, T.L. (1965) Elements of Queuing Theory and Its Application. Sovetskoe Radio, 510.
[3]	Cherkesov, G.N. (1974) Dependability of Technical Systems with Time Redundancy. Sovetskoe Radio, 296.
[4]	Feller, W. (1971) An Introduction to Probability Theory and Its Applications. Vol. 2, John Willey and Sons, New York, 766.
[5]	Mikadze, Z.I., Mikadze, I.S. and Khocholava, V.V. (2007) On One Multichannel Mixed Queuing System with Limited Waiting Time. Automatics and Telemechanics, 7, 44-51.
[6]	Khocholava, V.V. and Mikadze, I.S. (2002) On One Model of Queuing System. Georgian Engineering News, 4, 47-52.
[7]	Khurodze, R.A., Khocholava, V.V. and Mikadze, I.S. (2003) On One Queuing System with Unreliable Queuing System. Problems of Applied Mechanics, 3, 9-18.
[8]	Mikadze, I.S. and Khocholava, V.V. (2004) On One Model of Information Transition by Unreliable Communication Channel. Automatics and Telemechanics, 8, 85-90.
[9]	Mikadze, I.S., Khocholava, V.V. and Khurodze, R.A. (2004) Virtual Waiting Time in Single-Line QS with Unreliable Devices. Automatics and Telemechanics, 12, 119-128.
[10]	Khurodze, R.A. and Kakubava, R.V. (2005) Some Mathematical Aspects of Dependability Planning of Technical Systems. Bulletin of the Georgian Academy of Sciences, 171, 449-452.
[11]	Khurodze, R.A., Shamugia, R.R. and Kukava, R.R. (2006) Research of Dependability Characteristics of Technical Systems with Equipment and Time Duplications. Bulletin of the Georgian National Academy of Sciences, 174, 110-113.