Optimal steady-state and transient trajectories of multi-queue switching servers with a fixed service order of queues

Zwieten, D.A.J. van; Lefeber, Erjen; Adan, I.J.B.F.

doi:10.1016/j.peva.2015.11.003

Cited by 2 publications

(1 citation statement)

References 21 publications

(39 reference statements)

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“…We want to determine the optimal routeing policy for the incoming fluid so as to minimize this cost. Since the routeing policy does not affect the trajectory of z, the optimal policy needs to minimize the second integral if c > d, and maximize it if c < d. Related work on the optimal control of service (instead of routeing) in fluid systems can be found in [16], [26], and [30]. The optimal routeing policy for t ≥ T is obvious: keep sending the incoming fluid to the busy queue, and both the queues will remain empty forever.…”

Section: Optimal Control Of the Fluid Modelmentioning

confidence: 99%

Optimal routeing in two-queue polling systems

Adan¹,

Kulkarni

Lee

et al. 2018

J. Appl. Probab.

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We consider a polling system with two queues, exhaustive service, no switch-over times and exponential service times with rate µ in each queue. The waiting cost depends on the position of the queue relative to the server: It costs a customer c per time unit to wait in the busy queue (where the server is) and d per time unit in the idle queue (where no server is). Customers arrive according to a Poisson process with rate λ. We study the control problem of how arrivals should be routed to the two queues in order to minimize expected waiting costs and characterize individually and socially optimal routing policies under three scenarios of available information at decision epochs: no, partial and complete information. In the complete information case, we develop a new iterative algorithm to determine individually optimal policies, and show that such policies can be described by a switching curve. We conjecture that a linear switching curve is socially optimal, and prove that this policy is indeed optimal for the fluid version of the two-queue polling system. large body of research work in polling systems, and we refer the readers to a few survey papers for the full range of issues in polling systems that researchers have studied: see the book by Takagi [18], and the review papers of Levy and Sidi [13], Vishnevskii and Semenova [21] and Boon et al. [5].The early work considered a simple polling system consisting of a single server serving N queues in an exhaustive cyclic fashion, which means that it serves the customers in the i-th queue until it becomes empty and then moves to queue i + 1 (or 1 if i = N ). Results were obtained about the limiting distribution of the number of customers in the N queues, their means, and waiting times, and so on. These results were quickly extended to service policies other than exhaustive, such as e.g. gated, k-limited and Bernoulli, as well as non-cyclic server routing, non-zero switch over times, and so on. We refer the reader to the sources mentioned above for the detailed references.The issues of control of polling systems have received less attention than the performance analysis of polling systems. There are several possible control problems arising in polling systems. First, the order in which the queues are served can be determined to optimize system performance (such as weighted expected waiting times), assuming that the service discipline is fixed (such as exhaustive, or gated); see Boxma et al. [7], Yechiali [24], van der Wal and Yechiali [20]. When the server can switch after every service, the optimal dynamic service order is studied in greater detail, and may lead to simple rules like the cµ rule; for example, see Klimov [11,12], Haijema and van der Wal [9]. We refer to Vishnevskii and Semenova [21] for many more papers in this area.Customer routing in polling systems is a less studied area. Takine et al. [19], Sidi et al. [17] and Boon et al.[6] study a Jackson network style routing of customers among N queues, served cyclically by a single server. The control of custom...

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Section: Optimal Control Of the Fluid Modelmentioning

confidence: 99%