The Study of Equilibrium Strategies of the Unobservable Markovian Queue with Redundant Server for Balking and Delayed Repair

2021 ◽  
Vol 67 (2) ◽  
pp. 130-139
Author(s):  
Preeti Gautami Dubey ◽  
Shrivastava R K
Keyword(s):  
Equilibrium Strategies ◽  
Delayed Repair ◽  
Markovian Queue

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.

On a Markovian queue with weakly correlated interarrival times

1981 ◽  
Vol 18 (01) ◽  
pp. 190-203 ◽  
Author(s):  
Guy Latouche
Keyword(s):  
Time Distribution ◽  
Queueing System ◽  
Interarrival Time ◽  
Probability Vector ◽  
Common Value ◽  
Markovian Queue ◽  
The Stability ◽  
Number Of Customers ◽  
Stationary Probabilities ◽  
Stationary Probability Vector

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated. The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.

Impotence Following Delayed Repair of Prostatomembranous Urethral Disruption

1990 ◽  
Vol 144 (3) ◽  
pp. 677-678 ◽  
Author(s):  
C.B. Dhabuwala ◽  
Sayeed Hamid ◽  
Demetrios M. Katsikas ◽  
James M. Pierce
Keyword(s):  
Delayed Repair
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