Performance Analysis of a Markovian Queue with Impatient Customers and Working Vacation

2021 ◽  
Author(s):  
Shakir Majid
Keyword(s):  
Performance Analysis ◽  
Impatient Customers ◽  
Working Vacation ◽  
Markovian Queue

scholarly journals Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Cosmika Goswami ◽  
N. Selvaraju
Keyword(s):  
Blocking Probability ◽  
Death Process ◽  
Impatient Customers ◽  
Working Vacation ◽  
Multiple Working Vacations ◽  
Phase Type ◽  
Working Vacations ◽  
The One ◽  
Vacation Period ◽  
Stationary Probability Vector

We consider a PH/M/c queue with multiple working vacations where the customers waiting in queue for service are impatient. The working vacation policy is the one in which the servers serve at a lower rate during the vacation period rather than completely ceasing the service. Customer’s impatience is due to its arrival during the period where all the servers are in working vacations and the arriving customer has to join the queue. We formulate the system as a nonhomogeneous quasi-birth-death process and use finite truncation method to find the stationary probability vector. Various performance measures like the average number of busy servers in the system during a vacation as well as during a nonvacation period, server availability, blocking probability, and average number of lost customers are given. Numerical examples are provided to illustrate the effects of various parameters and interarrival distributions on system performance.

scholarly journals On Probability Characteristics for a Class of Queueing Models with Impatient Customers

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 594 ◽  
Author(s):  
Yacov Satin ◽  
Alexander Zeifman ◽  
Alexander Sipin ◽  
Sherif I. Ammar ◽  
Janos Sztrik
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Markov Model ◽  
Queueing Models ◽  
Impatient Customers ◽  
Numerical Examples ◽  
Markovian Queue ◽  
Proposed Model ◽  
System Characteristics ◽  
Individual Requirement

In this paper, a class of queueing models with impatient customers is considered. It deals with the probability characteristics of an individual customer in a non-stationary Markovian queue with impatient customers, the stationary analogue of which was studied previously as a successful approximation of a more general non-Markov model. A new mathematical model of the process is considered that describes the behavior of an individual requirement in the queue of requirements. This can be applied both in the stationary and non-stationary cases. Based on the proposed model, a methodology has been developed for calculating the system characteristics both in the case of the existence of a stationary solution and in the case of the existence of a periodic solution for the corresponding forward Kolmogorov system. Some numerical examples are provided to illustrate the effect of input parameters on the probability characteristics of the system.

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