scholarly journals OPTIMAL SWITCHING ON AND OFF THE ENTIRE SERVICE CAPACITY OF A PARALLEL QUEUE

2015 ◽  
Vol 29 (4) ◽  
pp. 483-506 ◽  
Author(s):  
Eugene A. Feinberg ◽  
Xiaoxuan Zhang
Keyword(s):  
Linear Programming ◽  
Finite Number ◽  
Optimal Policy ◽  
Average Cost ◽  
Optimization Problem ◽  
System Size ◽  
Single Server ◽  
Service Capacity ◽  
Optimal Switching ◽  
Holding Costs

This paper studies optimal switching on and off of the entire service capacity of an M/M/∞ queue with holding, running and switching costs. The running costs depend only on whether the system is on or off, and the holding costs are linear. The goal is to minimize average costs per unit time. The main result is that an average-cost optimal policy either always runs the system or is an (M, N)-policy defined by two thresholds M and N, such that the system is switched on upon an arrival epoch when the system size accumulates to N and is switched off upon a departure epoch when the system size decreases to M. It is shown that this optimization problem can be reduced to a problem with a finite number of states and actions, and an average-cost optimal policy can be computed via linear programming. An example, in which the optimal (M, N)-policy outperforms the best (0, N)-policy, is provided. Thus, unlike the case of single-server queues studied in the literature, (0, N)-policies may not be average-cost optimal.

scholarly journals SCHEDULING IN A SINGLE-SERVER QUEUE WITH STATE-DEPENDENT SERVICE RATES

2019 ◽  
Vol 34 (4) ◽  
pp. 507-521
Author(s):  
Urtzi Ayesta ◽  
Balakrishna Prabhu ◽  
Rhonda Righter
Keyword(s):  
Optimal Policy ◽  
Arrival Rate ◽  
Complete Characterization ◽  
Single Server ◽  
Holding Costs ◽  
Release Times ◽  
State Dependent ◽  
Service Rates ◽  
Transient System ◽  
The Cost

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.

scholarly journals Optimal stochastic scheduling of forest networks with switching penalties

1994 ◽  
Vol 26 (02) ◽  
pp. 474-497 ◽  
Author(s):  
Mark P. Van Oyen ◽  
Demosthenis Teneketzis
Keyword(s):  
Structural Properties ◽  
Optimal Policy ◽  
Switching Costs ◽  
Stochastic Scheduling ◽  
Single Server ◽  
Reward Rate ◽  
Holding Costs ◽  
Lump Sum ◽  
Optimal Policies ◽  
Set Up

We present structural properties of optimal policies for the problem of scheduling a single server in a forest network of N queues (without arrivals) subject to switching penalties. In addition to linear holding costs, we impose either lump sum switching costs or batch set-up delays which are incurred at each instant the server processes a job in a queue different from the previous one. We use reward rate notions to unearth conditions on the holding costs and service distributions for which an exhaustive policy is optimal. For the case of two nodes connected probabilistically in tandem, we explicitly define an optimal policy under similar conditions.

scholarly journals Average Cost Brownian Drift Control with Proportional Changeover Costs

2021 ◽  
Author(s):  
John H. Vande Vate
Keyword(s):  
Optimal Policy ◽  
Average Cost ◽  
Drift Rate ◽  
Optimality Criteria ◽  
Value Functions ◽  
Fixed Costs ◽  
Holding Costs ◽  
Practical Procedure ◽  
Long Run ◽  
Relative Value

This paper considers the problem of optimally controlling the drift of a Brownian motion with a finite set of possible drift rates so as to minimize the long-run average cost, consisting of fixed costs for changing the drift rate, processing costs for maintaining the drift rate, holding costs on the state of the process, and costs for instantaneous controls to keep the process within a prescribed range. We show that, under mild assumptions on the processing costs and the fixed costs for changing the drift rate, there is a strongly ordered optimal policy, that is, an optimal policy that limits the use of each drift rate to a single interval; when the process reaches the upper limit of that interval, the policy either changes to the next lower drift rate deterministically or resorts to instantaneous controls to keep the process within the prescribed range, and when the process reaches the lower limit of the interval, the policy either changes to the next higher drift rate deterministically or again resorts to instantaneous controls to keep the process within the prescribed range. We prove the optimality of such a policy by constructing smooth relative value functions satisfying the associated simplified optimality criteria. This paper shows that, under the proportional changeover cost assumption, each drift rate is active in at most one contiguous range and that the transitions between drift rates are strongly ordered. The results reduce the complexity of proving the optimality of such a policy by proving the existence of optimal relative value functions that constitute a nondecreasing sequence of functions. As a consequence, the constructive arguments lead to a practical procedure for solving the problem that is tens of thousands of times faster than previously reported methods.

scholarly journals Optimal stochastic scheduling of forest networks with switching penalties

1994 ◽  
Vol 26 (2) ◽  
pp. 474-497 ◽  
Author(s):  
Mark P. Van Oyen ◽  
Demosthenis Teneketzis
Keyword(s):  
Structural Properties ◽  
Optimal Policy ◽  
Switching Costs ◽  
Stochastic Scheduling ◽  
Single Server ◽  
Reward Rate ◽  
Holding Costs ◽  
Lump Sum ◽  
Optimal Policies ◽  
Set Up

We present structural properties of optimal policies for the problem of scheduling a single server in a forest network of N queues (without arrivals) subject to switching penalties. In addition to linear holding costs, we impose either lump sum switching costs or batch set-up delays which are incurred at each instant the server processes a job in a queue different from the previous one. We use reward rate notions to unearth conditions on the holding costs and service distributions for which an exhaustive policy is optimal. For the case of two nodes connected probabilistically in tandem, we explicitly define an optimal policy under similar conditions.

scholarly journals Sequential scheduling of priority queues and Arm-acquiring bandits

1987 ◽  
Vol 1 (2) ◽  
pp. 115-135 ◽  
Author(s):  
Chuanshu Ji
Keyword(s):  
Optimal Policy ◽  
Average Cost ◽  
Queueing Network ◽  
Single Server ◽  
Index Policy ◽  
Discounted Cost ◽  
Poisson Arrival ◽  
Long Run ◽  
Holding Cost ◽  
Arrival Processes

In a queueing network with a single server and r service nodes, a non-preemptive non-idling policy chooses a node to service at each service completion epoch. Under the assumptions of independent Poisson arrival processes, fixed routing probabilities, and linear holding cost rates, we apply Whistle's method for Arm-acquiring bandits to show that for minimizing discounted cost or long-run average cost the optimal policy is an index policy. We also give explicit expressions for those priority indices.

Monotonicity of Optimal Performance Measures for Polling Systems

1997 ◽  
Vol 11 (2) ◽  
pp. 219-228 ◽  
Author(s):  
Mark P. Van Oyen
Keyword(s):  
Optimal Policy ◽  
System Performance ◽  
Original System ◽  
Setup Time ◽  
Setup Times ◽  
Polling Systems ◽  
Single Server ◽  
Holding Costs ◽  
Setup Costs ◽  
Mean And Variance

We consider scheduling a single server in a multiclass queue subject to setup times and setup costs. We examine the issue of whether or not reductions in the mean and variance of the setup time distributions can lead to degraded system performance. Provided that setups are reduced according to a stochastically smaller ordering, we show that if an optimal policy is used both for the original system and for the system with reduced setup times, then an improvement in performance is guaranteed. Even in cases for which a truly optimal policy is unknown, idling can be employed to avoid degradation of performance as setup times are cut. We extend this approach to show that system performance is monotonic with respect to service time distributions, switching costs, holding costs, and uniform reductions in the arrival rates. Extensions to sequencedependent setups and job feedback are noted.

OPTIMAL CONTROL OF FLEXIBLE SERVERS IN TWO TANDEM QUEUES WITH OPERATING COSTS

2007 ◽  
Vol 22 (1) ◽  
pp. 107-131 ◽  
Author(s):  
Dimitrios G. Pandelis
Keyword(s):  
Optimal Control ◽  
Optimal Policy ◽  
Optimal Allocation ◽  
Operating Costs ◽  
Queuing Systems ◽  
Tandem Queues ◽  
Holding Costs ◽  
Flexible Servers ◽  
Tandem Queuing ◽  
Dedicated Servers

We consider two-stage tandem queuing systems with dedicated servers in each station and flexible servers that can serve in both stations. We assume exponential service times, linear holding costs, and operating costs incurred by the servers at rates proportional to their speeds. Under conditions that ensure the optimality of nonidling policies, we show that the optimal allocation of flexible servers is determined by a transition-monotone policy. Moreover, we present conditions under which the optimal policy can be explicitly determined.

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