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 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.

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.

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).

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.

scholarly journals Knowing What, How and Why: A Near Complete Solution for Aspect-Based Sentiment Analysis

2020 ◽  
Vol 34 (05) ◽  
pp. 8600-8607
Author(s):  
Haiyun Peng ◽  
Lu Xu ◽  
Lidong Bing ◽  
Fei Huang ◽  
Wei Lu ◽  
...  
Keyword(s):  
Sentiment Analysis ◽  
State Of The Art ◽  
Complete Solution ◽  
Unified Model ◽  
Two Stage ◽  
Fine Grained ◽  
Aspect Extraction ◽  
Second Stage ◽  
Opinion Extraction ◽  
Complete Story

Target-based sentiment analysis or aspect-based sentiment analysis (ABSA) refers to addressing various sentiment analysis tasks at a fine-grained level, which includes but is not limited to aspect extraction, aspect sentiment classification, and opinion extraction. There exist many solvers of the above individual subtasks or a combination of two subtasks, and they can work together to tell a complete story, i.e. the discussed aspect, the sentiment on it, and the cause of the sentiment. However, no previous ABSA research tried to provide a complete solution in one shot. In this paper, we introduce a new subtask under ABSA, named aspect sentiment triplet extraction (ASTE). Particularly, a solver of this task needs to extract triplets (What, How, Why) from the inputs, which show WHAT the targeted aspects are, HOW their sentiment polarities are and WHY they have such polarities (i.e. opinion reasons). For instance, one triplet from “Waiters are very friendly and the pasta is simply average” could be (‘Waiters’, positive, ‘friendly’). We propose a two-stage framework to address this task. The first stage predicts what, how and why in a unified model, and then the second stage pairs up the predicted what (how) and why from the first stage to output triplets. In the experiments, our framework has set a benchmark performance in this novel triplet extraction task. Meanwhile, it outperforms a few strong baselines adapted from state-of-the-art related methods.

On stochastic scheduling with precedence relations and switching costs

1980 ◽  
Vol 17 (4) ◽  
pp. 1016-1024 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Probability Distribution ◽  
Single Machine ◽  
Optimal Strategy ◽  
Switching Costs ◽  
Stochastic Scheduling ◽  
Random Variable ◽  
Precedence Relation ◽  
Precedence Relations

A collection of jobs is to be processed by a single machine. The amount of processing required by each job is a random variable with a known probability distribution. The jobs must be processed in a manner which is consistent with a precedence relation but the machine is free to switch from one job to another at any time; such switches are costly, however. This paper discusses conditions under which there is an optimal strategy for allocating the machine to the jobs which is given by a fixed permutation of the jobs indicating in which order they should be processed. When this is so, existing algorithms may be helpful in giving the best job ordering.

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