Abstract
In this paper we study a queueing model of assembly-like manufacturing operations. This study was motivated by an examination of a circuit pack testing procedure in an AT & T factory. However, the model may be representative of many manufacturing assembly operations. We assume that customers fromn classes arrive according to independent Poisson processes with the same arrival rate into a single-server queueing station where the service times are exponentially distributed. The service discipline requires that service be rendered simultaneously to a group of customers consisting of exactly one member from each class. The server is idle if there are not enough customers to form a group. There is a separate waiting area for customers belonging to the same class and the size of the waiting area is the same for all classes. Customers who arrive to find the waiting area for their class full, are lost. Performance measures of interest include blocking probability, throughput, mean queue length and mean sojourn time. Since the state space for this queueing system could be large, exact answers for even reasonable values of the parameters may not be easy to obtain. We have therefore focused on two approaches. First, we find upper and lower bounds for the mean sojourn time. From these bounds we obtain the asymptotic solutions as the arrival rate (waiting room, service rate) approaches zero (infinity). Second, for moderate values of these parameters we suggest an approximate solution method. We compare the results of our approximation against simulation results and report good correspondence.
Similar content being viewed by others
References
F. Baccelli and A. Makowski, Simple computable bounds for the fork-join queue,Proc. John Hopkins Conf. Info. Sciences (1985).
U.N. Bhat, Finite capacity assembly-like queues, Queueing Syst. Theor. and Appl. 1(1986)
F. Bonomi, private communication.
D. Gross and C.M. Harris,Fundamentals of Queueing Theory (Wiley, New York, 1974).
J.M. Harrison, Assembly-like queues, J. Appl. Prob. 10(1973)354.
B.R.K. Kashyap, A double ended queueing system with limited waiting space, Proc. Nat. Inst. Sci. India A31(1965)559.
G. Latouche, Queues with paired customers, J. Appl. Prob. 18(1981)684.
L. Flatto and S. Hahn, Two parallel queues created by arrivals with two demands, I, SIAM J. Appl. Math. 44, 5(1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lipper, E.H., Sengupta, B. Assembly-like queues with finite capacity: Bounds, asymptotics and approximations. Queueing Syst 1, 67–83 (1986). https://doi.org/10.1007/BF01149328
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01149328