We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression f...

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 p p e r considers a nunpreemptive priority queue with two classes of customers. Customers in each priority class arrive to the system according to a Markovian arrival process (MAP). Since the MAP is weakly dense in the class of stationary point processes, it is a fairly general arrival process. The service times of custcomers in ea,ch priority class are independent and identically distribu...

In this paper the MM ∑K k=1 CPPk/GE/c/L G-queue is introduced and proposed as a generalised Markovian node model in telecommunications networks. An exact and computationally efficient solution is obtained for the steady-state probabilities and performance measures. Issues concerning the computational effort are also discussed. The proposed queue is applied to the performance analysis of optical...

The equilibrium joint state probabilities of interacting Markov processes are obtained in a hierarchical way, by finding the reversed process of the interaction in terms of the reversed processes of the components. From a reversed process, a product-form solution for the joint state probabilities follows directly. The method uses a Markovian process algebra formalism and generalizes the recent ...

In this paper, we develop a simple analytical technique to determine P (fQ > qg), the tail of the queue length distribution, at an ATM multiplexer. The ATM multiplexer is modeled as a uid queue serving a large number of independent sources. Our method is based on the central limit theorem and the maximum variance approximation, and enables us to avoid the state explosion problem. The approach i...

Queueing soft hando attempts in DS-CDMA cellular systems can cause di erent e ects on system performance, compared with the hando attempts in TDMA and FDMA systems. This is because CDMA link capacity depends on other user interference which includes the power of blocked soft hando attempts. The power level of blocked soft hando attempts may be large because it cannot be controlled by a target b...

The equilibrium joint state probabilities of interacting Markov processes are obtained in a hierarchical way, by finding the reversed process of the interaction in terms of the reversed processes of its components. From a reversed process, a product-form solution for the joint state probabilities follows directly. The method uses a Markovian process algebra formalism and generalizes the recent ...

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix Q ≡ (qij)i,j=1. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time t ≥ 0, in t...

Vacation time queues with Markovian arrival process (MAP) are mainly useful in modeling and performance analysis of telecommunication networks based on asynchronous transfer mode (ATM) environment. This paper analyzes a single-server finite capacity queue wherein service is performed in batches of maximum size “b” with a minimum threshold “a” and arrivals are governed by MAP. The server takes a...