scholarly journals Equilibrium Joining Strategies of Delay-Sensitive Customers in a Queueing System with Service Quality Feedback

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Peng Liu ◽  
Jun Lv ◽  
Tao Jiang ◽  
Xudong Chai
Keyword(s):  
Service Quality ◽  
Queueing System ◽  
Queueing Systems ◽  
Optimal Strategies ◽  
System Parameters ◽  
Adjustment Procedure ◽  
Delay Sensitive ◽  
Quality Feedback ◽  
System Maintenance ◽  
Different Levels

In some queueing systems, customers are frequently asked for giving a service quality feedback for their service at their service completion instants. Based on this phenomenon, in this paper, we model this type of queueing systems as clearing queues with service quality feedback and system maintenance. Once the system receives an unsatisfied (negative) feedback from customers (i.e., a customer is unsatisfied with the service), the system undergoes an adjustment procedure, and at the same time, all the present customers are forced to leave the system. By considering the waiting cost and reward, we discuss the joining behavior of customers and, respectively, derive the corresponding equilibrium joining strategies and social optimal strategies under different levels of information (the observable and the unobservable cases). Finally, some numerical examples are provided to show the effect of several system parameters on the equilibrium and optimal balking strategies.

Optimal Strategy in Queueing Systems in Emergency Department

2018 ◽  
Vol 13 (1) ◽  
pp. 69-80
Author(s):  
Zeng Hui ◽  
Tian Ruiling ◽  
Liu Yupeng ◽  
Hou Yumei
Keyword(s):  
Emergency Department ◽  
Optimal Strategy ◽  
Queue Length ◽  
Queueing System ◽  
Queueing Systems ◽  
Optimal Strategies ◽  
Game Problem ◽  
Noncooperative Game ◽  
Service Interruption ◽  
Urgent Patient

The authors' study a noncooperative game problem for queueing control in emergency department (ED). One of the challenges to emergency department (ED) is the control of the urgent patients and the non-urgent patients. The urgent patient which is the primary customer, can be considered as the service interruption in a queueing system. The service interruptions occur frequently and can incur significant delays for the non-urgent patients. Therefore, a non-urgent patient needs to decide whether to join the queue or leave. The scenario is modeled as an M/M/1 queueing game with server interruption where each patient wants to optimize his benefit. It is shown that the individually optimal strategy for joining the queue is characterized by a threshold of queue length. The socially optimal threshold of queue length is also obtained. To bridge the gap between the individually and socially optimal strategies, a pricing mechanism is proposed to toll the service of each non-urgent patient, thus equalizing the two optimal strategies.

scholarly journals Equilibrium Joining Strategies in the Geo/GeoK/1 Queueing System

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1029
Author(s):  
Zaiming Liu ◽  
Can Cao ◽  
Shan Gao
Keyword(s):  
Strategic Behavior ◽  
Queueing System ◽  
Optimal Strategies ◽  
Social Benefit ◽  
System Parameters ◽  
Equilibrium Strategies ◽  
Linear Utility ◽  
Available Information ◽  
Linear Utility Function ◽  
The Impact

We study strategic behavior in the G e o / G e o K / 1 queueing system under both fully observable case and fully unobservable case. Furthermore, equilibrium and socially optimal strategies are obtained according to the available information and the linear utility function. We compare the impact of system parameters on the equilibrium strategies and socially optimal strategies. At the same time, we illustrate the effects of parameters on the obtained equilibrium social benefit. Finally, some numerical examples are presented.

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

ROBUST INTERVAL-BASED MINIMAX-REGRET ANALYSIS METHOD FOR FILTER MANAGEMENT OF FLUID POWER SYSTEM

2013 ◽  
Vol 30 (06) ◽  
pp. 1350021
Author(s):  
SONGLIN NIE ◽  
HUI JI ◽  
YEQING HUANG ◽  
ZHEN HU ◽  
YONGPING LI
Keyword(s):  
Power System ◽  
Optimal Strategies ◽  
Decision Makers ◽  
Fluid Power ◽  
Maintenance Cost ◽  
Minimax Regret ◽  
Fluid Power System ◽  
System Maintenance ◽  
Management Alternatives

Fluid contamination is one of the main reasons for the wear failure and the related downtime in a hydraulic power system. Filters play an important role in controlling the contamination effectively, increasing the reliability of the system, and maintaining the system economically. Due to the uncertainties of system parameters, the complicated relationship among components, as well as the lack of effective approach, managing filters is becoming one of the biggest challenges for engineers and decision makers. In this study, a robust interval-based minimax-regret analysis (RIMA) method is developed for the filter management in a fluid power system (FPS) under uncertainty. The RIMA method can handle the uncertainties existed in contaminant ingressions of the system and contaminant holding capacity of filters without making assumption on probabilistic distributions for random variables. Through analyzing the system cost of all possible filter management alternatives, an interval element regret matrix can be obtained, which enables decision makers to identify the optimal filter management strategy under uncertainty. The results of a case study indicate that the reasonable solutions generated can help decision makers understand the consequence of short-term and long-term decisions, identify optimal strategies for filter allocation and selection with minimized system-maintenance cost and system-failure risk.

On a property of a refusals stream

1997 ◽  
Vol 34 (03) ◽  
pp. 800-805 ◽  
Author(s):  
Vyacheslav M. Abramov
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Busy Period ◽  
Elementary Proof ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Wide Family

This paper consists of two parts. The first part provides a more elementary proof of the asymptotic theorem of the refusals stream for an M/GI/1/n queueing system discussed in Abramov (1991a). The central property of the refusals stream discussed in the second part of this paper is that, if the expectations of interarrival and service time of an M/GI/1/n queueing system are equal to each other, then the expectation of the number of refusals during a busy period is equal to 1. This property is extended for a wide family of single-server queueing systems with refusals including, for example, queueing systems with bounded waiting time.

COST ANALYSIS OF THE R-UNRELIABLE-UNLOADER QUEUEING SYSTEM

2008 ◽  
Vol 25 (01) ◽  
pp. 57-73
Author(s):  
KUO-HSIUNG WANG ◽  
CHUN-CHIN OH ◽  
JAU-CHUAN KE
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Queueing System ◽  
Cost Model ◽  
Analytic Solutions ◽  
Queueing Model ◽  
Exponential Distributions ◽  
System Parameters ◽  
Optimal Values ◽  
The Cost

This paper analyzes the unloader queueing model in which N identical trailers are unloaded by R unreliable unloaders. Steady-state analytic solutions are obtained with the assumptions that trip times, unloading times, finishing times, breakdown times, and repair times have exponential distributions. A cost model is developed to determine the optimal values of the number of unloaders and the finishing rate simultaneously, in order to minimize the expected cost per unit time. Numerical results are provided in which several steady-state characteristics of the system are calculated based on assumed numerical values given to the system parameters and the cost elements. Sensitivity analysis is also studied.

scholarly journals Convolution Model of a Queueing System with the cFIFO Service Discipline

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Sławomir Hanczewski ◽  
Adam Kaliszan ◽  
Maciej Stasiak
Keyword(s):  
Analytical Model ◽  
Queueing System ◽  
Queueing Systems ◽  
Service Discipline ◽  
Variable Bit Rate ◽  
Bit Rate ◽  
Simulation Experiments ◽  
Convolution Model ◽  
Theoretical Assumptions

This article presents an approximate convolution model of a multiservice queueing system with the continuous FIFO (cFIFO) service discipline. The model makes it possible to service calls sequentially with variable bit rate, determined by unoccupied (free) resources of the multiservice server. As compared to the FIFO discipline, the cFIFO queue utilizes the resources of a multiservice server more effectively. The assumption in the model is that the queueing system is offered a mixture of independent multiservice Bernoulli-Poisson-Pascal (BPP) call streams. The article also discusses the results of modelling a number of queueing systems to which different, non-Poissonian, call streams are offered. To verify the accuracy of the model, the results of the analytical calculations are compared with the results of simulation experiments for a number of selected queueing systems. The study has confirmed the accuracy of all adopted theoretical assumptions for the proposed analytical model.

scholarly journals Concavity of the throughput of tandem queueing systems with finite buffer storage space

1990 ◽  
Vol 22 (03) ◽  
pp. 764-767 ◽  
Author(s):  
Ludolf E. Meester ◽  
J. George Shanthikumar
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Sample Path ◽  
Concave Function ◽  
Time Interval ◽  
Single Server ◽  
Finite Buffer ◽  
Buffer Storage ◽  
Unlimited Supply ◽  
Number Of Customers

We consider a tandem queueing system with m stages and finite intermediate buffer storage spaces. Each stage has a single server and the service times are independent and exponentially distributed. There is an unlimited supply of customers in front of the first stage. For this system we show that the number of customers departing from each of the m stages during the time interval [0, t] for any t ≧ 0 is strongly stochastically increasing and concave in the buffer storage capacities. Consequently the throughput of this tandem queueing system is an increasing and concave function of the buffer storage capacities. We establish this result using a sample path recursion for the departure processes from the m stages of the tandem queueing system, that may be of independent interest. The concavity of the throughput is used along with the reversibility property of tandem queues to obtain the optimal buffer space allocation that maximizes the throughput for a three-stage tandem queue.

scholarly journals On the starshapeness of G/G/c queueing systems

1991 ◽  
Vol 23 (2) ◽  
pp. 431-435 ◽  
Author(s):  
J. George Shanthikumar ◽  
Couchen Wu
Keyword(s):  
Service Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Stage ◽  
Sojourn Times ◽  
Optimal Service ◽  
The Mean

In this paper we show that the waiting and the sojourn times of a customer in a single-stage, multiple-server, G/G/c queueing system are increasing and starshaped with respect to the mean service time. Usefulness of this result in the design of the optimal service speed in the G/G/c queueing system is also demonstrated.

On extremal service disciplines in single-stage queueing systems

1990 ◽  
Vol 27 (02) ◽  
pp. 409-416 ◽  
Author(s):  
Rhonda Righter ◽  
J. George Shanthikumar ◽  
Genji Yamazaki
Keyword(s):  
Service Time ◽  
Sojourn Time ◽  
Queueing System ◽  
Residual Life ◽  
Queueing Systems ◽  
Mean Residual Life ◽  
Service Discipline ◽  
Service Time Distribution ◽  
Service Disciplines ◽  
Number Of Customers

It is shown that among all work-conserving service disciplines that are independent of the future history, the first-come-first-served (FCFS) service discipline minimizes [maximizes] the average sojourn time in a G/GI/1 queueing system with new better [worse] than used in expectation (NBUE[NWUE]) service time distribution. We prove this result using a new basic identity of G/GI/1 queues that may be of independent interest. Using a relationship between the workload and the number of customers in the system with different lengths of attained service it is shown that the average sojourn time is minimized [maximized] by the least-attained-service time (LAST) service discipline when the service time has the decreasing [increasing] mean residual life (DMRL[IMRL]) property.

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