This paper considers three variants of last-come first-served (LCFS) preemptive service single-server queues, where customers are served under the LCFS preemptive resume (LCFS-PR), preemptive repeat-different (LCFS-PD), and preemptive repeat-identical (LCFS-PI) disciplines, respectively. These LCFS queues are fed by multiple batch Markovian arrival streams. Service times of customers from each ...

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...

A batch arrival single-server queueing system of a general type is considered. At the end of each busy period the server begins a multiple vacation period when the service process is stopped. A new approach to the study of departure process in such a system is proposed. Using the formula of total probability and renewal theory we direct the analysis to that in the system without vacations. An e...

In a typical wireless system, communications between a transmitter–receiver pair is subject to impairments such as intracell and intercell interference, as well as multipath fading. For practical wireless data transmission systems, e.g., UMTS or GPRS, it has been demonstrated by simulation and supported by real measurements that these impairments can be adequately modeled by hidden Markov model...

Rational Arrival Processes (RAPs) form a general class of stochastic processes which include Markovian Arrival Processes (MAPs) as a subclass. In this paper we study RAPs and their representations of different sizes. We show some transformation methods between different representations and present conditions to evaluate the size of the minimal representation. By using some analogous results fro...

We continue to focus on simple exponential approximations for steady-state tail probabilities in queues based on asymptotics. For the G/GI/1 model with i.i.d. service times that are independent of an arbitrary stationary arrival process, we relate the asymptotics for the steadystate waiting time, sojourn time and workload. We show that the three asymptotic decay rates coincide and that the thre...

We consider a two-stage tandem queue with single-server first station and multiserver second station. Customers arrive to Station 1 according to a batch Markovian arrival process BMAP . A batch may consist of heterogeneous customers. The type of a customer is determined upon completion of a service at Station 1. The customer’s type is classified based on the number of servers required to proces...