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1.
We study the effect of model uncertainties on optimal routing in a system of parallel queues. The uncertainty arises in modeling the service time distribution for the customers (jobs, packets) to be served. For a Poisson arrival process and Bernoulli routing, the optimal mean system delay generally depends on the variance of this distribution. However, as the input traffic load approaches the system capacity, the optimal routing assignment and corresponding mean system delay are shown to converge to a variance-invariant point. The implications of these results are examined in the context of gradient-based routing algorithms. An example of a model-independent algorithm using on-line gradient estimation is also included and its performance compared with that of model-based algorithms.This work was supported in part by the National Science Foundation under Grant ECS-88-01912, by the Office of Naval Research under Contract N00014-87-K-0304, and by NASA under Contract NAG 2-595.  相似文献   

2.
In this paper, we consider the routing problem described in Mohanty and Cassandras (Ref. 1). As in Ref. 1, we show that the optimal Bernoulli split to minimize mean time in the system is asymptotically independent of the variance of the service time. We give simple proofs of the results in that paper. We exploit the fact that the optimal split to minimize the mean queueing time is variance independent and the special structure of the Karush–Kuhn–Tucker optimality conditions to derive the optimal solution. Apart from being very straightforward, the proofs also give insight into the reason for the existence of the variance-independent asymptotically optimal routing policy.  相似文献   

3.
We consider a model of a multipath routing system where arriving customers are routed to a set of identical, parallel, single server queues according to balancing policies operating without state information. After completion of service, customers are required to leave the system in their order of arrival, thus incurring an additional resequencing delay. We are interested in minimizing the end-to-end delay (including time at the resequencing buffer) experienced by arriving customers. To that end we establish the optimality of the Round–Robin routing assignment in two asymptotic regimes, namely heavy and light traffic: In heavy traffic, the Round–Robin customer assignment is shown to achieve the smallest (in the increasing convex stochastic ordering) end-to-end delay amongst all routing policies operating without queue state information. In light traffic, and for the special case of Poisson arrivals, we show that Round–Robin is again an optimal (in the strong stochastic ordering) routing policy. We illustrate the stochastic comparison results by several simulation examples. The work of the first author was supported through an ARCHIMEDES grant by the Greek Ministry of Education. The work of the second author was prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government.  相似文献   

4.
Optimal static routing problems in open BCMP queueing networks with state-independent arrival and service rates are studied. They include static routing problems in communication networks and optimal static load balancing problems in distributed computer systems. We consider an overall optimal policy that is the routing policy whereby the overall mean response (or sojourn) time of a job is minimized. We obtain the routing decisions of the overall optimal policy and show that they may not be unique, but that the utilization of each service center is uniquely determined by the overall optimal policy. We also consider an individually optimal policy whereby jobs are routed so that each job may feel that its own expected response time is minimized if it knows the mean delay time for each path.  相似文献   

5.
We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are deterministic and the QoS metric is the probability a customer is queued, given by the Erlang-C formula. We use the Janssen–Van Leeuwaarden–Zwart bounds to obtain asymptotically optimal solutions to this problem. The second model considered is one in which the arrival rates are not completely known in advance (before the server staffing levels are chosen), but rather are known via a probability distribution. In this case, we provide asymptotically optimal solutions to the resulting stochastic integer program, leveraging results obtained for the case of deterministic arrivals.  相似文献   

6.
The following load balancing problem is investigated in discrete time: A service system consists of two service stations and two controllers, one in front of each station. The service stations provide the same service with identical service time distributions and identical waiting costs. Customers requiring service arrive at a controller's site and are routed to one of the two stations by the controller. The processes describing the two arrival streams are identical. Each controller has perfect knowledge of the workload in its own station and receives information about the other station's workload with one unit of delay. The controllers' routing strategies that minimize the customers' total flowtime are determined for a certain range of the parameters that describe the arrival process and the service distribution. Specifically, we prove that optimal routing strategies are characterized by thresholds that are either precisely specified or take one of two possible values.  相似文献   

7.
We study a system of several identical servers in parallel, where a routing decision must be made immediately on a job’s arrival. Jobs arrive according to a Poisson process, with their processing times following a discrete distribution with finite support. The processing time of a job is known on arrival and may be used in the routing decision. We propose a policy consisting of multi-layered round robin routing followed by shortest remaining processing time scheduling at the servers. This policy is shown to have a heavy traffic limit that is identical to one in which there is a single queue (no routing) and optimal heavy traffic scheduling. In light traffic, we show that the performance of this policy is worse than round robin routing followed by shortest remaining processing time scheduling. We also quantify the difference between round robin and multi-layered round robin routing, which in turn yields insights on the relative importance of routing versus (local) scheduling in such systems. AMS subject classifications: 68M20 · 60K25 (Work done while both authors were visitors at EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.)  相似文献   

8.
Chang  Junxia  Ayhan  Hayriye  Dai  J.G.  Xia  Cathy H. 《Queueing Systems》2004,48(3-4):263-307
We study the optimal dynamic scheduling of different requests of service in a multiclass stochastic fluid model that is motivated by recent and emerging computing paradigms for Internet services and applications. In particular, our focus is on environments with specific performance guarantees for each class under a profit model in which revenues are gained when performance guarantees are satisfied and penalties are incurred otherwise. Within the context of the corresponding fluid model, we investigate the dynamic scheduling of different classes of service under conditions where the workload of certain classes may be overloaded for a transient period of time. Specifically, we consider the case with two fluid classes and a single server whose capacity can be shared arbitrarily among the two classes. We assume that the class 1 arrival rate varies with time and the class 1 fluid can more efficiently reduce the holding cost. Under these assumptions, we characterize the optimal server allocation policy that minimizes the holding cost in the fluid model when the arrival rate function for class 1 is known. Using the insights gained from this deterministic case, we study the stochastic fluid system when the arrival rate function for class 1 is random and develop various policies that are optimal or near optimal under various conditions. In particular, we consider two different types of heavy traffic regimes and prove that our proposed policies are strongly asymptotically optimal. Numerical examples are also provided to demonstrate further that these policies yield good results in terms of minimizing the expected holding cost.  相似文献   

9.
Improved bounds are developed for a queue where arrivals are delayed by a fixed time. For moderate to heavy traffic, a simple improved upper bound is obtained which only uses the first two moments of the service time distribution. We show that our approach can be extended to obtain bounds for other types of delayed arrival queues. For very light traffic, asymptotically tight bounds can be obtained using more information about the service time distribution. While an improved upper bound can be obtained for light to moderate traffic it is not particularly easy to apply. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

10.
We address a rate control problem associated with a single server Markovian queueing system with customer abandonment in heavy traffic. The controller can choose a buffer size for the queueing system and also can dynamically control the service rate (equivalently the arrival rate) depending on the current state of the system. An infinite horizon cost minimization problem is considered here. The cost function includes a penalty for each rejected customer, a control cost related to the adjustment of the service rate and a penalty for each abandoning customer. We obtain an explicit optimal strategy for the limiting diffusion control problem (the Brownian control problem or BCP) which consists of a threshold-type optimal rejection process and a feedback-type optimal drift control. This solution is then used to construct an asymptotically optimal control policy, i.e. an optimal buffer size and an optimal service rate for the queueing system in heavy traffic. The properties of generalized regulator maps and weak convergence techniques are employed to prove the asymptotic optimality of this policy. In addition, we identify the parameter regimes where the infinite buffer size is optimal.  相似文献   

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