Computational analysis of steady-state probabilities of M/Ga,b/1 and related nonbulk queues

On a multilevel controlled bulk queueing system MX/Gr,R/1

“…The results obtained in the paper generalize, compliment or refine similar results existing in the literature [2,[6][7][8]11,12,21,23].…”

“…It is necessary to mention that unlike a model studied in [8] the authors of this paper do not assume the dependence of service on group sizes. [The latter option, however, was included and extensively studied in Dshalalow [14] and [15], and Dshalalow and Tadj [17][18][19], and it may be combined with all options set in the present paper.]…”

“…Special cases of e queueing system with service delay discipline appeared in Chaudhry and Templeton [7] and Chaudhry, Madill and Brire [8] without bulk input. The authors called them queueing systems with a quorum and denoted M/Ga'b/1.…”

“…A queueing system M/Ga'b/1 becomes more attractive (both theoretically and practically) if, in addition to the assumptions about quorum systems accepted in [7,8,23], the input stream is allowed to be bulk. In contrast with models of type M/Ga'b/1, in which the queue length, being less than a, will always (with probability 1) reach a, in systems MX/Ga'b/1 (with general bulk input) the probability of reaching exactly level a in similar situations is less than 1 (in most cases even very small).…”

Robustness of Rootfinding in Queueing Analyses

“…Chaudhry, Madill and Bri~re (1987) have shown that, for each n, (6) has exactly one root inside the unit circle. Powell (1985) used Newton's method in his work to find that root; but Chaudhry et al have had more (and complete) success using Muller's method, never having encountered any numerical difficulties.…”