Analysis of Queues in a Random Environment with Impatient Customers

We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.

Appointment scheduling with customer impatience based on operating cost model

An appointment scheduling problem is studied with the consideration of customer impatience.On the assumption that both the time of leaving queue and the time of service are exponentially distributed,in order to minimize the joint cost,the optimal appointment schedule of the fixed number of customers is studied.The joint cost function is composed of customers expected delay time and service availability time.The expected delay time of each customer in the queue is recursively computed in terms of customer interarrival time.Furthermore,the effect of impatience on the optimal schedule as well as the total operating cost is studied.The results show that as the impatience rate increases,the optimal interarrival time becomes shorter and the interarrival time of the last few customers gradually approaches that of the customers in the middle.In addition,impatient behaviors can increase the joint cost.

A Multi-server Queue in a Multi-phase Random Environment with Waiting Servers and Customers'Impatience Under Synchronous Working Vacation Policy

In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operative phase j,j=1,K¯,customers are served one by one.Once the system is empty,the servers have to wait a random period of time before leaving,causing the system to move to vacation phase 0 at which new arrivals can be served at lower rate.Using the method of the probability generating functions,we establish the steady-state analysis of the system.Special cases of the queueing model are presented.Then,explicit expressions of the useful system characteristics are derived.In addition,a cost model is constructed to define the optimal values of service rates,simultaneously,to minimize the total expected cost per unit time via a quadratic fit search method.Numerical examples are provided to display the impact of different system characteristics.

Finite Capacity Service System with Partial Server Breakdown and Recovery Policy:An Economic Perspective

Developing a comprehensive service strategy to optimize customer satisfaction presents an ongoing challenge for effective facility provider.The essence of comprehensive systems is selecting the suitable service design,establishing an effective service delivery process,and building continuous improvement.This research analyzes a finite capacity service system incorporating several realistic customer-server dynamics:customer impatience,server’s partial breakdown,and threshold recovery policy.When the number of customers is more,the server is under pressure to increase the service rate to mitigate the service system’s load.Motivating from this fact,the concept of service pressure condition is also incorporated.For characterization,we evaluate state probabilities derived using the matrix-analytic method and henceforth several performance measures.To address the cost optimization problem involving the developed Chapman-Kolmogorov forward differential-difference equations and determine optimal operational parameters,we employ the recently devised cuckoo search(CS)optimization approach.A comparative analysis is performed with the semi-classical optimizer:quasi-Newton(QN)method,and metaheuristics technique:particle swarm optimization(PSO),to validate the efficacy of results.Lastly,several numerical illustrations are depicted in different tables and graphs to understand essential characteristics quickly.