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.

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.

Optimal strategies and pricing analysis in M/M/1 queues with a single working vacation and multiple vacations

2020 ◽  
Vol 54 (6) ◽  
pp. 1593-1612
Author(s):  
Ruiling Tian ◽  
Yali Wang
Keyword(s):  
Optimal Strategies ◽  
Optimal Pricing ◽  
Single Server ◽  
Working Vacation ◽  
Numerical Examples ◽  
Multiple Vacations ◽  
The Social ◽  
Optimal Pricing Strategy ◽  
System States ◽  
Stationary Behavior

This paper considers the customers’ equilibrium and socially optimal joining-balking behavior in single-server Markovian queues with a single working vacation and multiple vacations. Arriving customers decide whether to join the system or balk based on the system states and a linear reward-cost structure, which incorporates the desire of customers for service and their dislike to wait. We consider that the system states are almost unobservable and fully unobservable, respectively. For these two 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 using numerical examples. We also study the pricing problem that maximizes the server’s profit and derive the optimal pricing strategy. Finally, the social benefits of the almost and fully unobservable queues are compared by numerical examples.

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.

scholarly journals A Discrete-Time Queue with Balking, Reneging, and Working Vacations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Veena Goswami
Keyword(s):  
Discrete Time ◽  
Cost Model ◽  
Single Server ◽  
Finite Buffer ◽  
Multiple Working Vacations ◽  
Optimal Service ◽  
Special Cases ◽  
Service Rates ◽  
Working Vacations ◽  
Vacation Period

This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically.

EQUILIBRIUM STRATEGIES IN STOCHASTIC GAMES WITH ADDITIVE COST AND TRANSITION STRUCTURE

1999 ◽  
Vol 01 (02) ◽  
pp. 131-147 ◽  
Author(s):  
HEINZ-UWE KÜENLE
Keyword(s):  
Weight Function ◽  
Stochastic Games ◽  
Optimal Strategies ◽  
Cost Structure ◽  
Equilibrium Strategy ◽  
Transition Structure ◽  
Equilibrium Strategies ◽  
Zero Sum ◽  
Action Spaces ◽  
Treated State

Two-person stochastic games with additive transition and cost structure and the criterion of expected total costs are treated. State space and action spaces are standard Borel, and unbounded costs are allowed. For the zero-sum case, it is shown that there are stationary deterministic εη-optimal strategies for every ε>0 and a certain weight function η if some semi-continuity and compactness conditions are fulfilled. Using these results, the existence of so-called quasi-stationary deterministic εη-equilibrium strategy pairs under corresponding conditions is proven.

Sign in / Sign up

Export Citation Format

Share Document