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1

Modelling customers’ impatience with discouraged arrival and retention of reneging

Medhi Pallabi

Operations Research and Decisions

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2021

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Vol. 31, No. 3

67--88

EN

The paper presents stochastic modelling of a single server, finite buffer Markovian queueing system with discouraged arrivals, baulking, reneging, and retention of reneged customers. The Markov process is used to derive the steady-state solution of the model. Closed-form expressions using probability generating functions (PGFs) are derived and presented for both classical and novel performance measures. In addition, a sensitivity analysis is carried out to study the effect of the system parameters on performance measures. A numerical problem is also presented to demonstrate the derived results and some design aspects.

2

Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy

Bouchentouf Amina Angelika, Yahiaoui Lahcene, Kadi Mokhtar, Majid Shakir

Operations Research and Decisions

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2020

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Vol. 30, No. 4

5--28

EN

This paper deals with customers’ impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers. Using the probability generating function (PGF) technique, we obtain the steady-state solution of the system. Besides, we prove the stochastic decomposition properties. Useful performance measures of the considered queueing system are derived. A cost model is developed. Then, the parameter optimisation is carried out numerically, using a quadratic fit search method (QFSM). Finally, numerical examples are provided to visualise the analytical results.

3

Optimization of an M/M/1/N feedback queue with retention of reneged customers

Kumar R., Jain N. K., Som B. K.

Operations Research and Decisions

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2014

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Vol. 24, No. 3

45--58

EN

Customer impatience has become a threat to the business world. Firms employ various customer retention strategies to retain their impatient (or reneged) customers. Customer retention mechanisms may help to retain some or all impatient customers. Further, due to unsatisfactory service, customers may rejoin a queue immediately after departure. Such cases are referred to as feedback customers. Kumar and Sharma take this situation into account and study an M/M/1/N feedback queuing system with retention of reneged customers. They obtain only a steady-state solution for this model. In this paper, we extend the work of Kumar and Sharma by performing an economic analysis of the model. We develop a model for the costs incurred and perform the appropriate optimization. The optimum system capacity and optimum service rate are obtained.

4

Stability of two families of real-time queueing networks

Kruk Ł.

Probability and Mathematical Statistics

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2008

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Vol. 28, Fasc. 2

179--202

EN

We study open multiclass queueing networks with renewal arrival streams and general service time distributions. Upon arrival to the network, customers from each class are assigned a random deadline drawn from a distribution associated with this class.We show that preemptive subcritical EDF networks with fixed customer routes are stable. We also prove that a broad class of (not necessarily subcritical) networks with reneging and Markovian routing, including EDF, FIFO, LIFO, SRPT, fixed priorities and processor sharing, is stable.