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 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 Optimality of index policies for stochastic scheduling with switching penalties

1992 ◽  
Vol 29 (04) ◽  
pp. 957-966 ◽  
Author(s):  
Mark P. Van Oyen ◽  
Dimitrios G. Pandelis ◽  
Demosthenis Teneketzis
Keyword(s):  
Optimal Policy ◽  
Time Delays ◽  
Stochastic Scheduling ◽  
Optimal Scheduling ◽  
Scheduling Policies ◽  
Parallel Queues ◽  
Lump Sum ◽  
Index Policies ◽  
Service Policy ◽  
The Impact

We investigate the impact of switching penalties on the nature of optimal scheduling policies for systems of parallel queues without arrivals. We study two types of switching penalties incurred when switching between queues: lump sum costs and time delays. Under the assumption that the service periods of jobs in a given queue possess the same distribution, we derive an index rule that defines an optimal policy. For switching penalties that depend on the particular nodes involved in a switch, we show that although an index rule is not optimal in general, there is an exhaustive service policy that is 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 USEFULNESS OF THE CONSTRAINED PLANNING PROBLEM IN A MODEL OF MONEY

2008 ◽  
Vol 12 (4) ◽  
pp. 503-525 ◽  
Author(s):  
Joydeep Bhattacharya ◽  
Rajesh Singh
Keyword(s):  
Government Policy ◽  
Optimal Policy ◽  
Policy Choice ◽  
Planning Problem ◽  
Equilibrium Concept ◽  
Limited Communication ◽  
Monetary Economy ◽  
Optimal Policies ◽  
Set Up ◽  
Planning Problems

In this paper, we study a decentralized monetary economy with a specified set of markets, rules of trade, an equilibrium concept, and a restricted set of policies and derive a set of equilibrium (monetary) allocations generated by these policies. Next we set up a simpler constrained planning problem in which we restrict the planner to choose from a set that contains the set of equilibrium allocations in the decentralized economy. If there is a government policy that allows the decentralized economy to achieve the constrained planner's allocation, then it is the optimal policy choice. To illustrate the power of such analyses, we solve such planning problems in three monetary environments with limited communication. The upshot is that solving constrained planning problems is potentially an extremely “efficient” (easy and quick) way of deriving optimal policies for the corresponding decentralized economies.

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 Optimal Multiserver Stochastic Scheduling of two Interconnected Priority Queues

1994 ◽  
Vol 26 (01) ◽  
pp. 258-279 ◽  
Author(s):  
Dimitrios G. Pandelis ◽  
Demosthenis Teneketzis
Keyword(s):  
Sufficient Conditions ◽  
Stochastic Scheduling ◽  
Random Variable ◽  
General Distribution ◽  
Single Server ◽  
Preemptive Scheduling ◽  
Discounted Cost ◽  
Holding Costs ◽  
Holding Cost ◽  
Server Problem

A number of jobs on two interconnected queues are to be processed by m identical servers. The servers operate in parallel, so that every server can process any job. Jobs in queue i, i = 1, 2, incur an instantaneous holding cost Ci during the time they remain in the system. The service time for jobs in queue i, denoted by Xi , is a random variable with a general distribution. The interconnection process is independent of the service process. We establish sufficient conditions on the service times, the holding costs and the interconnection process under which the non-preemptive scheduling strategy that gives priority to queue 1 minimizes the total expected α -discounted cost. We call this strategy P1. We present counterexamples showing that if any of the sufficient conditions is not satisfied P1 may not be optimal, and that the optimal policy for the single-server problem is not necessarily optimal for the multiserver problem.

scholarly journals Optimality of index policies for stochastic scheduling with switching penalties

1992 ◽  
Vol 29 (4) ◽  
pp. 957-966 ◽  
Author(s):  
Mark P. Van Oyen ◽  
Dimitrios G. Pandelis ◽  
Demosthenis Teneketzis
Keyword(s):  
Optimal Policy ◽  
Time Delays ◽  
Stochastic Scheduling ◽  
Optimal Scheduling ◽  
Scheduling Policies ◽  
Parallel Queues ◽  
Lump Sum ◽  
Index Policies ◽  
Service Policy ◽  
The Impact

We investigate the impact of switching penalties on the nature of optimal scheduling policies for systems of parallel queues without arrivals. We study two types of switching penalties incurred when switching between queues: lump sum costs and time delays. Under the assumption that the service periods of jobs in a given queue possess the same distribution, we derive an index rule that defines an optimal policy. For switching penalties that depend on the particular nodes involved in a switch, we show that although an index rule is not optimal in general, there is an exhaustive service policy that is optimal.

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.

scholarly journals Optimal Multiserver Stochastic Scheduling of two Interconnected Priority Queues

1994 ◽  
Vol 26 (1) ◽  
pp. 258-279 ◽  
Author(s):  
Dimitrios G. Pandelis ◽  
Demosthenis Teneketzis
Keyword(s):  
Sufficient Conditions ◽  
Stochastic Scheduling ◽  
Random Variable ◽  
General Distribution ◽  
Single Server ◽  
Preemptive Scheduling ◽  
Discounted Cost ◽  
Holding Costs ◽  
Holding Cost ◽  
Server Problem

A number of jobs on two interconnected queues are to be processed by m identical servers. The servers operate in parallel, so that every server can process any job. Jobs in queue i, i = 1, 2, incur an instantaneous holding cost Ci during the time they remain in the system. The service time for jobs in queue i, denoted by Xi, is a random variable with a general distribution. The interconnection process is independent of the service process. We establish sufficient conditions on the service times, the holding costs and the interconnection process under which the non-preemptive scheduling strategy that gives priority to queue 1 minimizes the total expected α -discounted cost. We call this strategy P1. We present counterexamples showing that if any of the sufficient conditions is not satisfied P1 may not be optimal, and that the optimal policy for the single-server problem is not necessarily optimal for the multiserver problem.

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