On the Shortest Queue Policy for the Tandem Parallel Queue

We consider two nodes in tandem. At each node or service centre there are two servers present with the same service rate μ and each with its own queue. Customers arrive at the first node according to a Poisson process with arrival rate λ. At their arrival, they have to be assigned to one of the servers, so they are routed to one of the queues at node 1. Customers leaving centre 1 enter node 2 and are routed to one of the queues at node 2 (see figure 1).

[1]  Wayne L. Winston.  OPTIMALITY OF THE SHORTEST LINE DISCIPLINE , 1977 .

[2]  Shlomo Halfin.  The shortest queue problem , 1985 .

[3]  D. Teneketzis,et al.  Routing in queueing networks under imperfect information: stochastic dominance and thresholds , 1989 .

[4]  B. W. Conolly,et al.  THE AUTOSTRADA QUEUEING PROBLEM , 1984 .

[5]  Richard F. Serfozo,et al.  Optimality of routing and servicing in dependent parallel processing systems , 1991, Queueing Syst. Theory Appl..

[6]  D. J. Houck,et al.  Comparison of Policies for Routing Customers to Parallel Queueing Systems , 1987, Oper. Res..

[7]  Ivo J. B. F. Adan,et al.  Analysis of the symmetric shortest queue problem , 1990 .

[8]  Ger Koole,et al.  On the Optimality of the Generalized Shortest Queue Policy , 1990, Probability in the Engineering and Informational Sciences.

[9]  Ward Whitt,et al.  Deciding Which Queue to Join: Some Counterexamples , 1986, Oper. Res..

[10]  Christos G. Cassandras,et al.  Optimal routing and buffer allocation for a class of finite capacity queueing systems , 1992 .

[11]  J. Ben Atkinson,et al.  An Introduction to Queueing Networks , 1988 .

[12]  Anthony Ephremides,et al.  A simple dynamic routing problem , 1980 .

[13]  R. Weber.  On the optimal assignment of customers to parallel servers , 1978, Journal of Applied Probability.

[14]  Pravin K. Johri,et al.  Optimality of the shortest line discipline with state-dependent service rates , 1989 .

[15]  Tapani Lehtonen.  Stochastic comparisons for many server queues , 1981 .

[16]  Vidyadhar G. Kulkarni,et al.  Optimal control of two parallel infinite-server queues , 1990, 29th IEEE Conference on Decision and Control.

[17]  B. Hajek.  Optimal control of two interacting service stations , 1982, 1982 21st IEEE Conference on Decision and Control.