Equilibrium and Socially Optimal Balking Strategies in Markovian Queues with Vacations and Sequential Abandonment

2016 ◽  
Vol 33 (05) ◽  
pp. 1650036 ◽  
Author(s):  
Gopinath Panda ◽  
Veena Goswami ◽  
Abhijit Datta Banik
Keyword(s):  
Performance Measures ◽  
Numerical Experiments ◽  
Optimal Strategies ◽  
Cost Structure ◽  
Single Server ◽  
System Parameters ◽  
Optimal Behavior ◽  
Markovian Queue ◽  
Queues With Vacations ◽  
The Individual

In this paper, we consider customers’ equilibrium and socially optimal behavior in a single-server Markovian queue with multiple vacations and sequential abandonments. Upon arrival customers decide for themselves whether to join or balk, based on the level of information available to them. During the server’s vacation, present customers become impatient and decide sequentially whether they will abandon the system or not upon the availability of a secondary transport facility. Assuming the linear reward-cost structure, we analyze the equilibrium balking strategies of customers under four cases: fully and almost observable as well as fully and almost unobservable. In all the above cases, the individual and social optimal strategies are derived. Finally, the dependence of performance measures on system parameters are demonstrated via numerical experiments.

STRATEGIC CUSTOMERS IN MARKOVIAN QUEUES WITH VACATIONS AND SYNCHRONIZED ABANDONMENT

2020 ◽  
Vol 62 (1) ◽  
pp. 89-120
Author(s):  
GOPINATH PANDA ◽  
VEENA GOSWAMI
Keyword(s):  
Cost Structure ◽  
Social Benefits ◽  
Single Server ◽  
Impatient Customers ◽  
Strategic Customers ◽  
Markovian Queue ◽  
The Social ◽  
Queues With Vacations ◽  
First Come First Serve ◽  
System Information

We study impatient customers’ joining strategies in a single-server Markovian queue with synchronized abandonment and multiple vacations. Customers receive the system information upon arrival, and decide whether to join or balk, based on a linear reward-cost structure under the acquired information. Waiting customers are served in a first-come-first-serve discipline, and no service is rendered during vacation. Server’s vacation becomes the cause of impatience for the waiting customers, which leads to synchronous abandonment at the end of vacation. That is, customers consider simultaneously but independent of others, whether to renege the system or to remain. We are interested to study the effect of both information and reneging choice on the balking strategies of impatient customers. We examine the customers’ equilibrium and socially optimal balking strategies under four cases of information: fully/almost observable and fully/almost unobservable cases, assuming the linear reward-cost structure. We compare the social benefits under all the information policies.

scholarly journals Equilibrium and Optimal Strategies in M/M/1 Queues with Working Vacations and Vacation Interruptions

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Ruiling Tian ◽  
Linmin Hu ◽  
Xijun Wu
Keyword(s):  
Optimal Strategies ◽  
Cost Structure ◽  
Single Server ◽  
Equilibrium Strategies ◽  
Markovian Queues ◽  
Multiple Working Vacations ◽  
Working Vacations ◽  
System States ◽  
Partially Observable ◽  
Stationary Behavior

We consider the customers equilibrium and socially optimal joining-balking behavior in single-server Markovian queues with multiple working vacations and vacation interruptions. Arriving customers decide whether to join the system or balk, based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness for waiting. We consider that the system states are observable, partially observable, and unobservable, respectively. For these cases, we first analyze the stationary behavior of the system and get the equilibrium strategies of the customers and compare them to socially optimal balking strategies numerically.

ON MARKOVIAN QUEUES WITH SINGLE WORKING VACATION AND BERNOULLI INTERRUPTIONS

2021 ◽  
pp. 1-28
Author(s):  
Ruiling Tian ◽  
Zhe George Zhang ◽  
Siping Su
Keyword(s):  
Optimal Strategies ◽  
Service Rate ◽  
Single Server ◽  
Working Vacation ◽  
Markovian Queue ◽  
Rate Period ◽  
System Information ◽  
Vacation Period ◽  
Maintenance Process ◽  
Different Levels

This paper considers the customers’ equilibrium and socially optimal joining–balking behavior in a single-server Markovian queue with a single working vacation and Bernoulli interruptions. The model is motivated by practical service systems where the service rate can be adjusted according to whether or not the system is empty. Specifically, we focus on a single-server queue in which the server's service rate is reduced from a regular to a lower one when the system becomes empty. This lower rate period is called a working vacation for the server which may represent that part of the service facility is under a maintenance process or works on other non-queueing job, or simply for saving the energy (for a machine server case). In this paper, we assume that the working vacation period is terminated after a random period or with probability p after serving a customer in a non-empty system. Such a system is called a queue with single working vacation and Bernoulli interruptions. Customers are strategic and can make choice of joining or balking based on different levels of system information. We consider four scenarios: fully observable, almost observable, almost unobservable, and fully unobservable queue cases. Under a reward-cost structure, we analyze the customer's equilibrium and social-optimal strategies. In addition, the effects of system parameters on optimal strategies are illustrated by numerical examples.

scholarly journals Equilibrium joining strategies in the single-server constant retrial queues with Bernoulli vacations

2019 ◽  
Author(s):  
Ke Sun ◽  
Jinting Wang
Keyword(s):  
Queue Length ◽  
Numerical Experiments ◽  
Retrial Queue ◽  
The State ◽  
Cost Structure ◽  
Retrial Queues ◽  
Single Server ◽  
Equilibrium Behavior ◽  
Information Level

We consider the equilibrium joining strategies in an M/M/1 constant retrial queue with Bernoulli vacations. There is no buffer in front of the server, thus an arriving customer will be served immediately if the server is available, and blocked ones wait in a queue if the server is busy or under vacation. The queue length information of orbit is observable to customers upon their arrivals. Then, blocked customers decide whether to join the orbit or not based on a reward-cost structure and their information level. After completing service, the server begins a vacation or remains available and it becomes available again when a vacation ends. The available server seeks to serve the customer in the head of the orbit queue. During the seeking process, an external arrival can interrupt it and obtain service. Our goal is to explore equilibrium behavior of customers in two information cases, fully observable case and almost observable case, which corresponding to whether blocked arrivals can differentiate the state of unavailable server. We obtain the threshold strategies of blocked customers in two information cases and provide numerical experiments to characterize the influence of different parameters on the equilibrium joining strategies.

scholarly journals Modelling customers’ impatience with discouraged arrival and retention of reneging

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Pallabi Medhi
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Stochastic Modelling ◽  
Steady State Solution ◽  
Single Server ◽  
Finite Buffer ◽  
System Parameters ◽  
Retention Of Reneged Customers

This paper presents stochastic modelling of a single server, finite buffer Markovian queuing system with discouraged arrivals, balking, reneging, and retention of reneged customers. Markov process is used to derive the steady-state solution of the model. Closed form expressions using probability generating functions (PGFs) are derived and presented for both classical and novel performance measures. In addition, a sensitivity analysis is carried out to study the effect of the system parameters on performance measures. A numerical problem is also presented to demonstrate the derived results and some design aspects.

scholarly journals The single server vacation queue with geometric abandonments and Bernoulli’s feedbacks

2018 ◽  
Vol 7 (2.21) ◽  
pp. 172
Author(s):  
V Vijayalakshmi ◽  
K Kalidass
Keyword(s):  
Performance Measures ◽  
Numerical Experiments ◽  
The State ◽  
Single Server ◽  
Server Vacation

In this article the behaviour of a single server vacation queue with geometric abandonments and Bernoulli’s feedbacks is carried out and various important performance measures are derived. Some numerical experiments are presented to study how the parameters of the model influence the state of the system. 

Customer Strategic Joining Behavior in Markovian Queues with Working Vacations and Vacation Interruptions Under Bernoulli Schedule

2019 ◽  
Vol 36 (01) ◽  
pp. 1950003
Author(s):  
Qingqing Ma ◽  
Yiqiang Q. Zhao ◽  
Weiqi Liu ◽  
Jihong Li
Keyword(s):  
Stationary Distribution ◽  
Optimal Strategies ◽  
Queuing System ◽  
Cost Structure ◽  
Single Server ◽  
Working Vacation ◽  
Equilibrium Strategies ◽  
Working Vacations ◽  
Bernoulli Schedule ◽  
Bernoulli Vacation

This study considers a single-server Markovian working vacation queuing system with Bernoulli vacation interruptions. Based on a linear reward-cost structure, the customer strategic joining behavior is analyzed under different information levels available to the arriving customers, namely fully observable, almost unobservable, and fully unobservable. For these cases, we first obtain the system stationary distribution. Thereafter, we determine the customer equilibrium strategies and compare them numerically with socially optimal strategies.

scholarly journals Equilibrium analysis of cloud user request based on the Markov queue with variable vacation and vacation interruption

2021 ◽  
Vol 55 (5) ◽  
pp. 2807-2825
Author(s):  
Yitong Zhang ◽  
Xiuli Xu
Keyword(s):  
Social Benefit ◽  
Equilibrium Analysis ◽  
Service Rate ◽  
Single Server ◽  
Working Vacation ◽  
Idle Period ◽  
Markovian Queue ◽  
User Request ◽  
Vacation Interruption ◽  
The Individual

This paper considers the equilibrium balking behavior of customers in a single-server Markovian queue with variable vacation and vacation interruption, where the server can switch across four states: vacation, working vacation, idle period, and busy period. Once the queue becomes empty, the server commences a working vacation and slows down its service rate. However, this period may be interrupted anytime by the vacation interruption. Upon the completion of a working vacation, the server takes a vacation in a probability-based manner and stops service if the system is empty. The system stays idle after a vacation until a new customer arrives. The comparisons between the equilibrium balking strategy of customers and the optimal expected social benefit per time unit for each type of queue are elucidated and the inconsistency between the individual optimization and the social optimization is revealed. Moreover, the sensitivity of the expected social benefit and the equilibrium threshold with respect to the several parameters as well as diverse precision levels is illustrated through numerical examples in a competitive cloud environment.

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

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