Optimal control of single-server queueing networks (original) (raw)

Optimal Control of Service Rates in Networks of Queues

Advances in Applied Probability, 1987

We prove a monotonicity result for the problem of optimal service rate control in certain queueing networks. Consider, as an illustrative example, a number of ·/M/1 queues which are arranged in a cycle with some number of customers moving around the cycle. A holding cost hi (xi ) is charged for each unit of time that queue i contains xi customers, with hi being convex. As a function of the queue lengths the service rate at each queue i is to be chosen in the interval , where cost ci (μ) is charged for each unit of time that the service rate μis in effect at queue i. It is shown that the policy which minimizes the expected total discounted cost has a monotone structure: namely, that by moving one customer from queue i to the following queue, the optimal service rate in queue i is not increased and the optimal service rates elsewhere are not decreased. We prove a similar result for problems of optimal arrival rate and service rate control in general queueing networks. The results are ...

Structural properties of the optimal resource allocation policy for single-queue systems

Annals of Operations Research, 2013

This paper studies structural properties of the optimal resource allocation policy for singlequeue systems. Jobs arrive at a service facility and are sent one by one to a pool of computing resources for parallel processing. The facility poses a constraint on the maximum expected sojourn time of a job. A central decision maker allocates the servers dynamically to the facility. We consider two models: a limited resource allocation model, where the allocation of resources can only be changed at the start of a new service, and a fully flexible allocation model, where the allocation of resources can also change during a service period. In these two models, the objective is to minimize the average utilization costs whilst satisfying the time constraint. To this end, we cast these optimization problems as Markov decision problems and derive structural properties of the relative value function. We show via dynamic programming that (1) the optimal allocation policy has a work-conservation property, and (2) the optimal number of servers follows a step function with as extreme policy the bang-bang control policy.

Optimal control for multi-servers queueing systems under periodic review

1977

This paper deals with the problem of finding the optimal dynamic operating policy for an M/M/S queue. The svstem is observed periodically, and a t the beginning of each period the system controller selects the number of service units to be kept open during that period. The optimality criterion used is the total discounted cost over a finite horixon.

Scheduling in a Single-Server Queue with State-Dependent Service Rates

Probability in the Engineering and Informational Sciences, 2019

We consider single-server scheduling to minimize holding costs where the capacity, or rate of service, depends on the number of jobs in the system, and job sizes become known upon arrival. In general, this is a hard problem, and counter-intuitive behavior can occur. For example, even with linear holding costs the optimal policy may be something other than SRPT or LRPT, it may idle, and it may depend on the arrival rate. We first establish an equivalence between our problem of deciding which jobs to serve when completed jobs immediately leave, and a problem in which we have the option to hold on to completed jobs and can choose when to release them, and in which we always serve jobs according to SRPT. We thus reduce the problem to determining the release times of completed jobs. For the clearing, or transient system, where all jobs are present at time 0, we give a complete characterization of the optimal policy and show that it is fully determined by the cost-to-capacity ratio. With arrivals, the problem is much more complicated, and we can obtain only partial results. We show that if the cost-to-capacity ratio is linear, then all nonidling policies yield the same average cost. We further characterize the optimal policy in some special cases. For example, we show that as long as capacity is increasing in the number of jobs, LRPT stochastically minimizes the mean busy period.

Near optimal control of queueing networks over a finite horizon

Annals of Operations Research, 2008

We propose a novel approach for controlling queueing networks that minimizes weighted holding costs over a finite time horizon. Our approach approximates the discrete problem by a fluid system for which an optimization problem is formulated. This problem is a separated continuous linear program, it is solved optimally using a simplex based algorithm of Weiss. The solution consists of piecewise constant allocations of the activities, with a finite number of breakpoints over the time horizon. Once solved, we associate a multi-class queueing network with infinite virtual queues with each interval of the fluid solution, and this measures the deviations of the original system from the fluid solution. We then track the fluid solution by using an adaptation of Dai and Lin's maximum pressure policy that keeps these deviations rate stable. This procedure is asymptotically optimal as we scale up the number of jobs and the processing speed. We illustrate the details of the approach on a simple example composed of two servers and three queues. Simulation results confirm that the system performance is near optimal when the network is scaled up.

Near optimal control of queueing networks over a finite time horizon

Annals of Operations Research, 2009

Effect of the server capacity distribution on the optimal control of a bulk service queueing system

Chaos, Solitons & Fractals, 2003

ABSTRACT In this paper the optimal control of a single-channel bulk service queueing system with random server capacity is investigated. Given an accumulation level r, the server stops processing new customers whenever the queue falls below r and resumes service when the queue reaches level r again. Server capacity becomes random following an idle period. A quick search procedure is designed to determine the value of r that yields the minimum expected total cost per unit of time. The effect of the server capacity distribution on the optimal control is then studied. Finally, a sensitivity analysis is conducted in order to assess the extent to which our results are valid.

Optimal Control of Queueing Systems with Heterogeneous Servers

Queueing Systems, 2004

An optimal policy to minimize the queue length in a multi-server controllable queueing system with heterogeneous servers has a threshold property, and it uses the fastest server if necessary (see and ). This study gives a numerical description of optimal policies that minimize the operational cost for such a system.

On the optimality of a full-service policy for a queueing system with discounted costs

Mathematical Methods of Operations Research, 2005

We provide weak sufficient conditions for a full-service policy to be optimal in a queueing control problem in which the service rate is a dynamic decision variable. In our model there are service costs and holding costs and the objective is to minimize the expected total discounted cost over an infinite horizon. We begin with a semi-Markov decision model for a single-server queue with exponentially distributed inter-arrival and service times. Then we present a general model with weak probabilistic assumptions and demonstrate that the full-service policy minimizes both finite-horizon and infinite-horizon total discounted cost on each sample path.

Optimal control of single-server queueing networks (original) (raw)

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