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.
