caa a22 4500 386350493 CHVBK 20180307111827.0 cr unu---uuuuu 161130e198910 xx s 000 0 eng 10.1017/S0269964800001364 doi S0269964800001364 pii (NATIONALLICENCE)cambridge-10.1017/S0269964800001364 Tandem Conveyor Queues [Elektronische Daten] This paper analyzes a queueing system in which a constant-speed conveyor brings new items for service and carries away served items. The conveyor is a sequence of cells each able to hold at most one item. At each integer time, a new cell appears at the queue's input position. This cell holds an item requiring service with probability a, holds a passerby requiring no service with probability b, and is empty with probability (1- a - b). Service times are integers synchronized with the arrival of cells at the input, and they are geometrically distributed with parameter μ. Items requiring service are placed in an unbounded queue to await service. Served items are put in a second unbounded queue to await replacement on the conveyor in cells at the input position. Two models are considered. In one, a served item can only be placed into a cell that was empty on arrival; in the other, the served item can be placed into a cell that was either empty or contained an item requiring service (in the latter case unloading and loading at the input position can take place in the same time unit). The stationary joint distribution of the numbers of items in the two queues is studied for both models. It is verified that, in general, this distribution does not have a product form. Explicit results are worked out for special cases, e.g., when b = 0, and when all service times are one time unit (μ = 1). It is shown how the analysis of the general problem can be reduced to the solution of a Riemann boundary-value problem. Copyright © Cambridge University Press 1989 Baccelli F. International de Recherche en Informatique et en Automatique 06565 Valbonne Cedex, France Coffman E.G. AT&T Bell Laboratories Murray Hill, New Jersey 07974 Gilbert E.N. AT&T Bell Laboratories Murray Hill, New Jersey 07974 Probability in the Engineering and Informational Sciences Cambridge University Press 3/4(1989-10), 517-536 0269-9648 3:4<517 1989 3 PES https://doi.org/10.1017/S0269964800001364 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0269964800001364 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baccelli F. International de Recherche en Informatique et en Automatique 06565 Valbonne Cedex, France NATIONALLICENCE 700 1- Coffman E.G. AT&T Bell Laboratories Murray Hill, New Jersey 07974 NATIONALLICENCE 700 1- Gilbert E.N. AT&T Bell Laboratories Murray Hill, New Jersey 07974 NATIONALLICENCE 773 0- Probability in the Engineering and Informational Sciences Cambridge University Press 3/4(1989-10), 517-536 0269-9648 3:4<517 1989 3 PES CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge