THE N-NETWORK MODEL WITH UPGRADES

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.

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DYNAMIC CONTROL OF A SINGLE-SERVER SYSTEM WHEN JOBS CHANGE STATUS

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964817000213 ◽

2017 ◽

Vol 32 (3) ◽

pp. 353-395

Author(s):

Gabriel Zayas-Cabán ◽

Hyun-Soo Ahn

Keyword(s):

Queueing Systems ◽

Dynamic Control ◽

Sufficient Conditions ◽

Single Server ◽

Priority Rules ◽

Holding Costs ◽

Class 1 ◽

Markov Decision ◽

Service Rates ◽

Customer Model

From health care to maintenance shops, many systems must contend with allocating resources to customers or jobs whose initial service requirements or costs change when they wait too long. We present a new queueing model for this scenario and use a Markov decision process formulation to analyze assignment policies that minimize holding costs. We show that the classic cμ rule is generally not optimal when service or cost requirements can change. Even for a two-class customer model where a class 1 task becomes a class 2 task upon waiting, we show that additional orderings of the service rates are needed to ensure the optimality of simple priority rules. We then show that seemingly-intuitive switching curve structures are also not optimal in general. We study these scenarios and provide conditions under which they do hold. Lastly, we show that results from the two-class model do not extend to when there are n≥3 customer classes. More broadly, we find that simple priority rules are not optimal. We provide sufficient conditions under which a simple priority rule holds. In short, allowing service and/or cost requirements to change fundamentally changes the structure of the optimal policy for resource allocation in queueing systems.

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

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964802164047 ◽

2002 ◽

Vol 16 (4) ◽

pp. 453-469 ◽

Cited By ~ 46

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.

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OPTIMAL ADMISSION CONTROL IN QUEUES WITH WORKLOAD-DEPENDENT SERVICE RATES

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964806060335 ◽

2006 ◽

Vol 20 (4) ◽

pp. 543-570 ◽

Cited By ~ 10

Author(s):

René Bekker ◽

Sem C. Borst

Keyword(s):

Admission Control ◽

Production Systems ◽

Control Policy ◽

Threshold Value ◽

Service Rate ◽

Qualitative Behavior ◽

Threshold Policy ◽

Long Run ◽

Service Rates ◽

Admission Control Policy

We consider a queuing system with a workload-dependent service rate. We specifically assume that the service rate is first increasing and then decreasing as a function of the amount of work. The latter qualitative behavior is quite common in practical situations, such as production systems. The admission of work into the system is controlled by a policy for accepting or rejecting jobs, depending on the state of the system. We seek an admission control policy that maximizes the long-run throughput. Under certain conditions, we show that a threshold policy is optimal, and we derive a criterion for determining the optimal threshold value.

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Undiscounted Control Policy Generation for Continuous-Valued Optimal Control by Approximate Dynamic Programming

International Journal of Control ◽

10.1080/00207179.2021.1939892 ◽

2021 ◽

pp. 1-35

Author(s):

Jonathan Lock ◽

Tomas McKelvey

Keyword(s):

Optimal Control ◽

Dynamic Programming ◽

Approximate Dynamic Programming ◽

Control Policy

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An experimental study of Web switching behavior

Human Systems Management ◽

10.3233/hsm-2003-22204 ◽

2003 ◽

Vol 22 (2) ◽

pp. 87-93

Author(s):

James Otto ◽

Mohammad Najdawi ◽

William Wagner

Keyword(s):

Experimental Study ◽

Electronic Commerce ◽

Web Site ◽

Waiting Times ◽

Switching Behavior ◽

The Internet ◽

Wait Times ◽

Web Page ◽

Extensive Growth ◽

The Impact

With the extensive growth of the Internet and electronic commerce, the issue of how users behave when confronted with long download times is important. This paper investigates Web switching behavior. The paper describes experiments where users were subjected to artificially delayed Web page download times to study the impact of Web site wait times on switching behavior. Two hypotheses were tested. First, that longer wait times will result in increased switching behavior. The implication being that users become frustrated with long waiting times and choose to go elsewhere. Second, that users who switch will benefit, in terms of decreased download times, from their decision to switch.

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Online Ratings of Primary Care Physicians: Comparison of Gender, Training, and Specialty

Journal of Patient Experience ◽

10.1177/23743735211007700 ◽

2021 ◽

Vol 8 ◽

pp. 237437352110077

Author(s):

Daliah Wachs ◽

Victoria Lorah ◽

Allison Boynton ◽

Amanda Hertzler ◽

Brandon Nichols ◽

...

Keyword(s):

Primary Care ◽

Primary Care Physicians ◽

Waiting Times ◽

Wait Time ◽

Primary Care Providers ◽

Wait Times ◽

Care Providers ◽

Female Physicians ◽

Online Ratings ◽

And Gender

The purpose of this study was to explore patient perceptions of primary care providers and their offices relative to their physician’s philosophy (medical degree [MD] vs doctorate in osteopathic medicine [DO]), specialty (internal medicine vs family medicine), US region, and gender (male vs female). Using the Healthgrades website, the average satisfaction rating for the physician, office parameters, and wait time were collected and analyzed for 1267 physicians. We found female doctors tended to have lower ratings in the Midwest, and staff friendliness of female physicians were rated lower in the northwest. In the northeast, male and female MDs were rated more highly than DOs. Wait times varied regionally, with northeast and northwest regions having the shortest wait times. Overall satisfaction was generally high for most physicians. Regional differences in perception of a physician based on gender or degree may have roots in local culture, including proximity to a DO school, comfort with female physicians, and expectations for waiting times.

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

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964808000077 ◽

2007 ◽

Vol 22 (1) ◽

pp. 107-131 ◽

Cited By ~ 8

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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