We consider a single-server queue with exponential service
time and two types of arrivals: positive and negative. Positive
customers are regular ones who form a queue and a negative arrival
has the effect of removing a positive customer in the system.
In many applications, it might be more appropriate to assume
the dependence between positive arrival and negative arrival.
In order to reflect the dependence, we assume that the positive
arrivals and negative arrivals are governed by a finite-state
Markov chain with two absorbing states, say 0 and 0′. The
epoch of absorption to the states 0 and 0′ corresponds to
an arrival of positive and negative customers, respectively. The
Markov chain is then instantly restarted in a transient state,
where the selection of the new state is allowed to depend on the
state from which absorption occurred.The Laplace–Stieltjes transforms (LSTs) of the sojourn
time distribution of a customer, jointly with the probability
that the customer completes his service without being removed,
are derived under the combinations of service disciplines FCFS
and LCFS and the removal strategies RCE and RCH. The service
distribution of phase type is also considered.
Finite state Markov-chain approximations to highly persistent processes
