Analysis of the busy period in threshold control system. (English. Russian original) Zbl 1186.93069

Autom. Remote Control 71, No. 1, 87-104 (2010); translation from Avtom. Telemekh. 2010, No. 1, 99-117 (2010).
Summary: Consideration is given to controllable Markov queuing systems with nonhomogeneous servers and threshold policy of server activation depending on the queue length. By the busy period is meant the time interval between the instant of customer arrival to the empty system and the instant of service completion when the system again becomes free. The system busy period and the number of serviced customers are analyzed. Recurrent relations for the distribution density in terms of the Laplace transform and generating function, as well as formulas for calculation of the corresponding arbitrary-order moments, are obtained.


93E03 Stochastic systems in control theory (general)
90B22 Queues and service in operations research
60J28 Applications of continuous-time Markov processes on discrete state spaces
Full Text: DOI


[1] Larsen, R.L. and Agrawala, A.K., Control of a Heterogeneous Two-server Exponential Queuing System, IEEE Trans. Soft. Eng., 1983, vol. 9, pp. 526–552. · Zbl 0517.90031
[2] Lin, W. and Kumar, P.R., Optimal Control of a Queuing System with Two Heterogeneous Servers, IEEE Trans. Automat. Control, 1984, vol. 29, pp. 696–703. · Zbl 0546.90035
[3] Rykov, V.V., On Monotonicity Conditions for Optimal Policies for Controlling Queuing Systems, Autom. Remote Control, 1999, no. 9, pp. 1290–1301. · Zbl 1058.60080
[4] Efrosinin, D.V. and Rykov, V.V., Numerical Study of the Optimal Control of a System with Nonhomogeneous Servers, Autom. Remote Control, 2003, no. 2, pp. 302–309. · Zbl 1071.60086
[5] Morrison, J.A., Two-server Queue with One Server Idle Below a Threshold, Queuing Syst., 1990, vol. 7, pp. 325–336. · Zbl 0713.60102
[6] Efrosinin, D.V. and Rykov, V.V., On Performance Characteristics for Queueing Systems with Heterogeneous Servers, Autom. Remote Control, 2008, no. 1, pp. 61–75. · Zbl 1156.93028
[7] Artalejo, J.R. and Economou, A., Markovian Controllable Queuing Systems with Hysteretic Policies: Busy Period and Waiting Time Analysis, Method. Comput. Appl. Probab., 2005, vol. 7, pp. 353–378. · Zbl 1084.60052
[8] Kleinrock, L., Queuing Systems, vol. 1: Theory, New York: Wiley, 1975. · Zbl 0334.60045
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.