We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that o -periods in the arrival process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a nite-bu...

This paper considers a discrete-time queue with gated priority. Low priority customers arrive at the first queue at the gate in batches according to a batch Bernoulli process (BBP). When the gate opens, all low priority customers at the first queue move to the second queue at a single server. On the other hand, high priority customers directly join the second queue upon arrival. The arrival pro...

Many problems in management science and telecommunications can be solved by the analysis of a D/D/1 queueing model. In this paper, we use the zeros, both inside and outside the unit circle, of the denominator of the generating function of the model to obtain an explicit closed-form solution for the equilibrium probabilities of the number of customers in the system. The moments of the number of ...

This paper considers a discrete-time queue with a gate. The system has a single server and a gate. Customers arrive to the system according to a batch Bernoulli process and wait for the next gate opening in front of the gate. When the gate opens, all the customers who are waiting at the gate move into the inside of the gate. The server serves the customers only inside the gate. The gate closes ...

This paper studies a discrete-time queueing system where each customer has a maximum allowed sojourn time in the system, referred to as the “deadline” of the customer. More specifically, we model the deadlines of the consecutive customers as independent and geometrically distributed random variables. Customers enter the system according to a general independent arrival process, i.e., the number...