The regularities of queues in models with infinite waiting room

E. A. Danielyan ; A. A. Danielyan ; I. E. Danielyan

Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2006), pp. 3-23

Résumé

In the present paper the developments of Queueing Theory is described, its belongness to Operations Research and Probability Theory is substantiated. The Regularities of Many Servers Queues with infinite waiting room are explained on the example of $GI|G|s|\infty$ model. The explicit formulas, limit theorems in fixed and heavy traffic conditions, stability, inequalities for the main characteristics, extremal problems are presented. The main attention in future is given to $GI|G|1|\infty$ model with FIFO service discipline. Not only known results are formulated but also some results, which were established by authors. For instance, in $GI | G|1|\infty$ model two groups of assumptions are suggested, which lead to the Little formulas. In particular, $M | G|1|\infty$ model is considered.