Transient Analysis of a Multi-server Queuing Model with Discouraged Arrivals and Retention of Reneging Customers

2017 ◽  
pp. 54-64
Author(s):  
Rakesh Kumar ◽  
Sapana Sharma
Keyword(s):  
Transient Analysis ◽  
Queuing Model ◽  
Multi Server

scholarly journals Zero Queueing for Multi-Server Jobs

2021 ◽  
Vol 5 (1) ◽  
pp. 1-25
Author(s):  
Weina Wang ◽  
Qiaomin Xie ◽  
Mor Harchol-Balter
Keyword(s):  
Cloud Computing ◽  
Stability Region ◽  
Transient Analysis ◽  
Queueing Systems ◽  
Sufficient Conditions ◽  
Hard Problem ◽  
Queueing Model ◽  
Multiple Servers ◽  
First Results ◽  
Multi Server

Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-server-per-job model: an arrival might not "fit'' into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.

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.

scholarly journals A Multi-Server Queuing Model With Balking and Correlated Reneging With Application in Health Care Management

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 169623-169639
Author(s):  
Godlove Suila Kuaban ◽  
Rakesh Kumar ◽  
Bhavneet Singh Soodan ◽  
Piotr Czekalski
Keyword(s):  
Health Care ◽  
Care Management ◽  
Health Care Management ◽  
Queuing Model ◽  
Multi Server

scholarly journals Mathematical analysis of single queue multi server and multi queue multi server queuing models: comparison study

2015 ◽  
Vol 3 (3) ◽  
pp. 97 ◽  
Author(s):  
Vijay Prasad ◽  
Badshah V.H ◽  
Tariq Ahmad Koka
Keyword(s):  
Mathematical Analysis ◽  
Comparison Study ◽  
Queuing Model ◽  
Total Cost ◽  
Queuing Models ◽  
Models Comparison ◽  
Mathematical Equations ◽  
Expected Total Cost ◽  
Multi Server ◽  
Better Than

<p>In the research paper entitled Mathematical Analysis of Single Queue Multi Server and Multi Queue Multi Server Queuing Model, Prasad and Badshah [7] were proved that single queue multi server model is better than multi queue multi server model, and discussed the relation between the performance measures of these two models, and derive the mathematical equations. In this paper we derive the total cost with assumption of certain Waiting cost in both cases. Also, prove that the expected total cost is less for single queue multi server model as comparing with multi queue multi server model.</p>

scholarly journals A Precise Study on Solving the Multi Server Queuing Model through Lpp By Using Python Program

2020 ◽  
Vol 993 ◽  
pp. 012109
Author(s):  
S Vijay Prasad ◽  
Ranadheer Donthi ◽  
Mahesh Kumar Challa
Keyword(s):  
Queuing Model ◽  
Multi Server ◽  
Precise Study

scholarly journals The Sensitivity Analysis of Service and Waiting Costs of A Multi Server Queuing Model

2020 ◽  
Vol 993 ◽  
pp. 012107
Author(s):  
S Vijay Prasad ◽  
Ranadheer Donthi ◽  
Mahesh Kumar Challa
Keyword(s):  
Sensitivity Analysis ◽  
Queuing Model ◽  
Multi Server
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