Transient solution of a multi-server queue with catastrophes and impatient customers when system is down

2014 ◽  
Vol 8 ◽  
pp. 4585-4592 ◽  
Author(s):  
G. Arul Freeda Vinodhini ◽  
V. Vidhya
Keyword(s):  
Transient Solution ◽  
Impatient Customers ◽  
Server Queue ◽  
Multi Server

scholarly journals On optimal stochastic jumps in multi server queue with impatient customers via stochastic control

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ali Delavarkhalafi
Keyword(s):  
Optimal Control ◽  
Complete Information ◽  
Queuing System ◽  
Arrival Process ◽  
Impatient Customers ◽  
Time Intervals ◽  
Poisson Arrival ◽  
Server Queue ◽  
Multi Server ◽  
Request Service

<p style='text-indent:20px;'>In this paper, a queuing system as multi server queue, in which customers have a deadline and they request service from a random number of identical severs, is considered. Indeed there are stochastic jumps, in which the time intervals between successive jumps are independent and exponentially distributed. These jumps will be occurred due to a new arrival or situation change of servers. Therefore the queuing system can be controlled by restricting arrivals as well as rate of service for obtaining optimal stochastic jumps. Our model consists of a single queue with infinity capacity and multi server for a Poisson arrival process. This processes contains deterministic rate <inline-formula><tex-math id="M1">\begin{document}$ \lambda(t) $\end{document}</tex-math></inline-formula> and exponential service processes with <inline-formula><tex-math id="M2">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> rate. In this case relevant customers have exponential deadlines until beginning of their service. Our contribution is to extend the Ittimakin and Kao's results to queueing system with impatient customers. We also formulate the aforementioned problem with complete information as a stochastic optimal control. This optimal control law is found through dynamic programming.</p>

scholarly journals M/M/c/N queuing systems with encouraged arrivals, reneging, retention and feedback customers

2018 ◽  
Vol 28 (3) ◽  
pp. 333-344 ◽  
Author(s):  
Bhupender Som ◽  
Sunny Seth
Keyword(s):  
System Size ◽  
Stationary System ◽  
Queuing Systems ◽  
Impatient Customers ◽  
Queuing Model ◽  
Special Cases ◽  
Multi Server ◽  
Measures Of Performance

Customers often get attracted by lucrative deals and discounts offered by firms. These, attracted customers are termed as encouraged arrivals. In this paper, we developed a multi-server Feedback Markovian queuing model with encouraged arrivals, customer impatience, and retention of impatient customers. The stationary system size probabilities are obtained recursively. Also, we presented the necessary measures of performance and gave numerical illustrations. Some particular, and special cases of the model are discussed.

scholarly journals Analysis of Multi-Server Queue with Self-Sustained Servers

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2134
Author(s):  
Alexander Dudin ◽  
Olga Dudina ◽  
Sergei Dudin ◽  
Konstantin Samouylov
Keyword(s):  
Three Dimensional ◽  
Optimal Choice ◽  
Arrival Process ◽  
Queuing Model ◽  
Numerical Result ◽  
Self Sufficiency ◽  
Server Queue ◽  
Markov Arrival ◽  
Markov Arrival Process ◽  
Multi Server

A novel multi-server vacation queuing model is considered. The distinguishing feature of the model, compared to the standard queues, is the self-sufficiency of servers. A server can terminate service and go on vacation independently of the system manager and the overall situation in the system. The system manager can make decisions whether to allow the server to start work after vacation completion and when to try returning some server from a vacation to process customers. The arrival flow is defined by a general batch Markov arrival process. The problem of optimal choice of the total number of servers and the thresholds defining decisions of the manager arises. To solve this problem, the behavior of the system is described by the three-dimensional Markov chain with the special block structure of the generator. Conditions for the ergodicity of this chain are derived, the problem of computation of the steady-state distribution of the chain is discussed. Expressions for the key performance indicators of the system in terms of the distribution of the chain states are derived. An illustrative numerical result is presented.

Analysis of an infinite multi-server queue with an optional service

2013 ◽  
Vol 65 (2) ◽  
pp. 216-225 ◽  
Author(s):  
Jau-Chuan Ke ◽  
Chia-Huang Wu ◽  
Wen Lea Pearn
Keyword(s):  
Optional Service ◽  
Server Queue ◽  
Multi Server
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