This paper discusses a discrete-time queueing system in which an arriving customer may adopt four different strategies; two of them correspond to a LCFS discipline where displacements or expulsions occur, and in the other two, the arriving customer decides to follow a FCFS discipline or to become a negative customer eliminating the customer in the server, if any. The different choices of the involved parameters make this model to enjoy a great versatility, having several special cases of interest. We carry out a thorough analysis of the system, and using a generating function approach, we derive analytical results for the stationary distributions obtaining performance measures for the number of customers in the queue and in the system. Also, recursive formulae for calculating the steady-state distributions of the queue and system size has been developed. Making use of the busy period of an auxiliary system, the sojourn times of a customer in the queue and in the system have also been obtained. Finally, some numerical examples are given.
Discrete-time system Decision problem Trigger customers Negative customers
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Krishnamoorthy, A., Gopakumar, B., Viswanath Narayanan, V.: A retrial queue with server interruptions, resumption and restart of service. Operations Research International Journal 12, 133–149 (2012)zbMATHGoogle Scholar
Krishnamoorthy, A., Pramod, P., Chakravarthy, S.: A note on characterizing service interruptions with phase-type distribution. Journal of Stochastic Analysis and Applications 31(4), 671–683 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
Piórkowski, A., Werewka, J.: Minimization of the total completion time for asinchronous transmission in a packet data-transmission system. Int. J. Appl. Math. Comput. Sci. 20, 391–400 (2010)CrossRefzbMATHGoogle Scholar
Walraevens, J., Steyaert, B., Bruneel, H.: A preemptive repeat priority queue with resampling: performance analysis. Ann. Oper. Res. 146, 189–202 (2006)MathSciNetCrossRefzbMATHGoogle Scholar