scholarly journals Analysis of Equilibrium Strategies in Markovian Queues With Negative Customers and Working Breakdowns

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 159868-159878 ◽  
Author(s):  
Ruiling Tian ◽  
Yali Wang
Keyword(s):  
Negative Customers ◽  
Equilibrium Strategies ◽  
Markovian Queues

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 closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

scholarly journals Optimal Pricing Strategies and Customers’ Equilibrium Behavior in an Unobservable M/M/1 Queueing System with Negative Customers and Repair

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Doo Ho Lee
Keyword(s):  
Queueing System ◽  
Point Of View ◽  
Optimal Pricing ◽  
Pricing Strategies ◽  
Negative Customers ◽  
Economic Point ◽  
Equilibrium Behavior ◽  
Payment Scheme ◽  
Ex Post ◽  
Pricing Schemes

This work investigates the optimal pricing strategies of a server and the equilibrium behavior of customers in an unobservable M/M/1 queueing system with negative customers and repair. In this work, we consider two pricing schemes. The first is termed the ex-post payment scheme, where the server charges a price that is proportional to the time spent by a customer in the system. The second scheme is the ex-ante payment scheme, where the server charges a flat rate for all services. Based on the reward-cost structure, the server (or system manager) should make optimal pricing decisions in order to maximize its expected profit per time unit in each payment scheme. This study also investigates equilibrium joining/balking behavior under the server’s optimal pricing strategies in the two pricing schemes. We show, given a customer’s equilibrium, that the two pricing schemes are perfectly identical from an economic point of view. Finally, we illustrate the effect of several system parameters on the optimal joining probabilities, the optimal price, and the equilibrium behavior via numerical examples.

A QUEUE WITH POSITIVE AND NEGATIVE ARRIVALS GOVERNED BY A MARKOV CHAIN

2003 ◽  
Vol 17 (4) ◽  
pp. 487-501 ◽  
Author(s):  
Yang Woo Shin ◽  
Bong Dae Choi
Keyword(s):  
Markov Chain ◽  
Transient State ◽  
Single Server ◽  
Negative Customers ◽  
Service Distribution ◽  
Finite State ◽  
Sojourn Time Distribution ◽  
Absorbing States ◽  
Negative Arrivals ◽  
Selection Of

We consider a single-server queue with exponential service time and two types of arrivals: positive and negative. Positive customers are regular ones who form a queue and a negative arrival has the effect of removing a positive customer in the system. In many applications, it might be more appropriate to assume the dependence between positive arrival and negative arrival. In order to reflect the dependence, we assume that the positive arrivals and negative arrivals are governed by a finite-state Markov chain with two absorbing states, say 0 and 0′. The epoch of absorption to the states 0 and 0′ corresponds to an arrival of positive and negative customers, respectively. The Markov chain is then instantly restarted in a transient state, where the selection of the new state is allowed to depend on the state from which absorption occurred.The Laplace–Stieltjes transforms (LSTs) of the sojourn time distribution of a customer, jointly with the probability that the customer completes his service without being removed, are derived under the combinations of service disciplines FCFS and LCFS and the removal strategies RCE and RCH. The service distribution of phase type is also considered.

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