论文信息 - An Optimal Multithreshold Control for the Input Flow of the GI/PH/1 Queueing System with a BMAP Flow of Negative Customers

An Optimal Multithreshold Control for the Input Flow of the GI/PH/1 Queueing System with a BMAP Flow of Negative Customers

A GI/PH/1 queueing system with an additional flow of negative customers is studied. The system has many operation modes differing in the distribution of inter-arrival lengths. Mode control depends on the queue length at arrival instants defined by a multithreshold strategy. The stationary state probability distribution of the system for fixed thresholds is studied. Numerical examples are given to illustrate the determination of the optimal threshold set in a fixed search domain.

[1] Erhan Çinlar,et al. Introduction to stochastic processes , 1974 .

[2] Srinivas R. Chakravarthy. The Batch Markovian Arrival Process: A Review and Future Work , 2001 .

[3] Henk C. Tijms,et al. On the Optimality of a Switch- Over Policy for Controlling the Queue Size in an M/G/1 Queue with Varibale Service Rate , 1975, Optimization Techniques.

[4] David M. Lucantoni,et al. New results for the single server queue with a batch Markovian arrival process , 1991 .

[5] Marcel F. Neuts,et al. Matrix-Geometric Solutions in Stochastic Models , 1981 .

[6] H. R. Gail,et al. Spectral analysis of M/G/1 and G/M/1 type Markov chains , 1996, Advances in Applied Probability.

[7] Alexander N. Dudin,et al. Optimal admission control in a queueing system with heterogeneous traffic , 2003, Oper. Res. Lett..

[8] P. P. Bocharov,et al. G-Networks: Development of the Theory of Multiplicative Networks , 2003 .

[9] P. P. Bocharov,et al. The Stationary Characteristics of the G/MSP/1/r Queueing System , 2003 .