OPTIMAL CONTROL OF A TWO-STAGE TANDEM QUEUING SYSTEM WITH FLEXIBLE SERVERS

2002 ◽  
Vol 16 (4) ◽  
pp. 453-469 ◽  
Author(s):  
Hyun-soo Ahn ◽  
Izak Duenyas ◽  
Mark E. Lewis
Keyword(s):  
Optimal Control ◽  
Numerical Study ◽  
Queuing System ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Flexible Servers ◽  
Carry Over ◽  
Tandem Queuing ◽  
New Jobs

We consider the optimal control of two parallel servers in a two-stage tandem queuing system with two flexible servers. New jobs arrive at station 1, after which a series of two operations must be performed before they leave the system. Holding costs are incurred at rate h1 per unit time for each job at station 1 and at rate h2 per unit time for each job at station 2.The system is considered under two scenarios; the collaborative case and the noncollaborative case. In the prior, the servers can collaborate to work on the same job, whereas in the latter, each server can work on a unique job although they can work on separate jobs at the same station. We provide simple conditions under which it is optimal to allocate both servers to station 1 or 2 in the collaborative case. In the noncollaborative case, we show that the same condition as in the collaborative case guarantees the existence of an optimal policy that is exhaustive at station 1. However, the condition for exhaustive service at station 2 to be optimal does not carry over. This case is examined via a numerical study.

scholarly journals A complete solution for the optimal stochastic scheduling of a two-stage tandem queue with two flexible servers

2005 ◽  
Vol 42 (03) ◽  
pp. 778-796 ◽  
Author(s):  
Klaus Schiefermayr ◽  
Josef Weichbold
Keyword(s):  
Optimal Control ◽  
Optimal Strategy ◽  
Complete Solution ◽  
Stochastic Scheduling ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Processing Times ◽  
Flexible Servers

We consider a two-stage tandem queue with two parallel servers and two queues. We assume that initially all jobs are present and that no further arrivals take place at any time. The two servers are identical and can serve both types of job. The processing times are exponentially distributed. After being served, a job of queue 1 joins queue 2, whereas a job of queue 2 leaves the system. Holding costs per job and per unit time are incurred if there are jobs holding in the system. Our goal is to find the optimal strategy that minimizes the expected total holding costs until the system is cleared. We give a complete solution for the optimal control of all possible parameters (costs and service times), especially for those parameter regions in which the optimal control depends on how many jobs are present in the two queues.

scholarly journals A complete solution for the optimal stochastic scheduling of a two-stage tandem queue with two flexible servers

2005 ◽  
Vol 42 (3) ◽  
pp. 778-796 ◽  
Author(s):  
Klaus Schiefermayr ◽  
Josef Weichbold
Keyword(s):  
Optimal Control ◽  
Optimal Strategy ◽  
Complete Solution ◽  
Stochastic Scheduling ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Processing Times ◽  
Flexible Servers

We consider a two-stage tandem queue with two parallel servers and two queues. We assume that initially all jobs are present and that no further arrivals take place at any time. The two servers are identical and can serve both types of job. The processing times are exponentially distributed. After being served, a job of queue 1 joins queue 2, whereas a job of queue 2 leaves the system. Holding costs per job and per unit time are incurred if there are jobs holding in the system. Our goal is to find the optimal strategy that minimizes the expected total holding costs until the system is cleared. We give a complete solution for the optimal control of all possible parameters (costs and service times), especially for those parameter regions in which the optimal control depends on how many jobs are present in the two queues.

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.

Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

1999 ◽  
Vol 31 (04) ◽  
pp. 1095-1117 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Study ◽  
Stochastic Scheduling ◽  
Static Case ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Cross Training ◽  
Dynamic Case ◽  
Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

1999 ◽  
Vol 31 (4) ◽  
pp. 1095-1117 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Study ◽  
Stochastic Scheduling ◽  
Static Case ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Cross Training ◽  
Dynamic Case ◽  
Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

THE N-NETWORK MODEL WITH UPGRADES

2010 ◽  
Vol 24 (2) ◽  
pp. 171-200 ◽  
Author(s):  
Douglas G. Down ◽  
Mark E. Lewis
Keyword(s):  
Optimal Control ◽  
Numerical Study ◽  
Waiting Times ◽  
Control Policy ◽  
Wait Times ◽  
Threshold Policy ◽  
Holding Costs ◽  
Class 1 ◽  
Service Rates ◽  
Flexible Server

In this article we introduce a new method of mitigating the problem of long wait times for low-priority customers in a two-class queuing system. To this end, we allow class 1 customers to be upgraded to class 2 after they have been in queue for some time. We assume that there are ci servers at station i, i=1, 2. The servers at station 1 are flexible in the sense that they can work at either station, whereas the servers at station 2 are dedicated. Holding costs at rate hi are accrued per customer per unit time at station i, i=1, 2. This study yields several surprising results. First, we show that stability analysis requires a condition on the order of the service rates. This is unexpected since no such condition is required when the system does not have upgrades. This condition continues to play a role when control is considered. We provide structural results that include a c-μ rule when an inequality holds and a threshold policy when the inequality is reversed. A numerical study verifies that the optimal control policy significantly reduces holding costs over the policy that assigns the flexible server to station 1. At the same time, in most cases the optimal control policy reduces waiting times of both customer classes.

THE OPTIMAL CONTROL OF A GENERAL TANDEM QUEUE

2006 ◽  
Vol 20 (2) ◽  
pp. 307-327 ◽  
Author(s):  
Josef Weichbold ◽  
Klaus Schiefermayr
Keyword(s):  
Optimal Control ◽  
Sufficient Condition ◽  
Scheduling Problem ◽  
Tandem Queue ◽  
Holding Costs ◽  
System A ◽  
Flexible Servers

We consider a scheduling problem with two interconnected queues and two flexible servers. It is assumed that all jobs are present at the beginning and that there are no further arrivals to the system at any time. For each job, there are waiting costs per unit of time until the job leaves the system. A job of queue 1, after being served, joins queue 2 with probability p and leaves the system with probability 1 − p. The objective is how to allocate the two servers to the queues such that the expected total holding costs until the system is empty are minimized. We give a sufficient condition such that for any number of jobs in queue 1 and queue 2, it is optimal to allocate both servers to queue 1 (resp. queue 2).

scholarly journals Fast Two-Stage Computation of an Index Policy for Multi-Armed Bandits with Setup Delays

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 52
Author(s):  
José Niño-Mora
Keyword(s):  
Numerical Study ◽  
Arithmetic Operation ◽  
Bandit Problem ◽  
Index Policy ◽  
Two Stage ◽  
Second Stage ◽  
Whittle Index ◽  
Set Up ◽  
Computing Method ◽  
Special Case

We consider the multi-armed bandit problem with penalties for switching that include setup delays and costs, extending the former results of the author for the special case with no switching delays. A priority index for projects with setup delays that characterizes, in part, optimal policies was introduced by Asawa and Teneketzis in 1996, yet without giving a means of computing it. We present a fast two-stage index computing method, which computes the continuation index (which applies when the project has been set up) in a first stage and certain extra quantities with cubic (arithmetic-operation) complexity in the number of project states and then computes the switching index (which applies when the project is not set up), in a second stage, with quadratic complexity. The approach is based on new methodological advances on restless bandit indexation, which are introduced and deployed herein, being motivated by the limitations of previous results, exploiting the fact that the aforementioned index is the Whittle index of the project in its restless reformulation. A numerical study demonstrates substantial runtime speed-ups of the new two-stage index algorithm versus a general one-stage Whittle index algorithm. The study further gives evidence that, in a multi-project setting, the index policy is consistently nearly optimal.

scholarly journals Measuring Energy Performance for Regional Sustainable Development in China: A New Framework based on a Dynamic Two-Stage SBM Approach

2020 ◽  
Vol 12 (7) ◽  
pp. 2851 ◽  
Author(s):  
Sheng-Hsiung Chiu ◽  
Tzu-Yu Lin ◽  
Hai-Lan Yang
Keyword(s):  
Economic Growth ◽  
Sustainable Development ◽  
Co2 Emissions ◽  
Energy Performance ◽  
Portfolio Performance ◽  
Low Carbon ◽  
Two Stage ◽  
Regional Economic ◽  
Regional Sustainable Development ◽  
Carry Over

Sustainable development has always been an important issue for all policy makers, even more so now, as global warming has seriously threatened the whole world. To understand the efficacy of regional sustainable policies, we proposed a dynamic, two-stage, slacks-based measure (SBM) model with carry-over and intermediate variables, highlighting the importance of an electricity portfolio, to measure overall energy performance for the purpose of regional sustainable development. In this unified linear programming framework with intertemporal evaluation, we estimated the effects of a clean electricity supply by the abatement of CO2 emissions and the gain of economic growth. The results can be used as a reference for decision makers to shape regional sustainable development policies. Using data of 30 provincial administration regions in China for the period of 2012–2017, we postulate that the lower energy performance of the Chinese regional economic system for sustainable development may be attributed to a lower electricity portfolio performance. We then postulate that investment in low-carbon energy infrastructure can combat CO2 emissions, and is also a major driving force in the regional economic growth.

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