Control policies for the MX/g/1 queueing system
Management Science
Batch arrival queue with N-policy and single vacation
Computers and Operations Research
SUPPLEMENTARY VARIABLE TECHNIQUE IN STOCHASTIC MODELS
Probability in the Engineering and Informational Sciences
Analysis of a two phase queueing system with general service times
Operations Research Letters
A two-phase queueing system with server vacations
Operations Research Letters
Operations Research Letters
Analysis of a retrial queue with two-phase service and server vacations
Queueing Systems: Theory and Applications
The N-policy for an unreliable server with delaying repair and two phases of service
Journal of Computational and Applied Mathematics
A repairable queueing model with two-phase service, start-up times and retrial customers
Computers and Operations Research
Expert Systems with Applications: An International Journal
Controlling arrival and service of a two-removable-server system using genetic algorithm
Expert Systems with Applications: An International Journal
Mathematical and Computer Modelling: An International Journal
Analysis of an infinite multi-server queue with an optional service
Computers and Industrial Engineering
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We consider a batch arrival queueing system, where the server provides two stages of heterogeneous service with a modified Bernoulli schedule under N-policy. The server remains idle till the queue size becomes N (= 1). As soon as the queue size becomes at least N, the server instantly starts working and provides two stages of service in succession to each customer, i.e., the first stage service followed by the second stage service. However, after the second stage service, the server may take a vacation or decide to stay in the system to provide service to the next customer, if any. We derive the queue size distribution at a random epoch as well as a departure epoch under the steady state conditions. Further, we demonstrate the existence of the stochastic decomposition property to show that the departure point queue size distribution of this model can be decomposed into the distributions of three independent random variables. We also derive some important performance measures of this model. Finally, we develop a simple procedure to obtain optimal stationary operating policy under a suitable linear cost structure.