An embedded Markov chain is used to analyze a G/M/1 queuing system with N policy. When the system is empty, the server remains idle (deactivates) and does not start serving the waiting customers in the queue until the number of arrivals reaches N. The service is performed in batches of min(n, N) if there are n customers waiting at the completion of service. Service times of the server depend o...

Traac on high-speed networks is expected to bèbursty'. This has spurred interest in the queueing properties of bursty traac models, such as Markov additive processes. These processes have by now been studied extensively by many authors, but almost exclusively in the innnite buuer setting. This paper deals with the case of a nite-buuered queue loaded with bursty traac. It shows how to calculate ...

A class of nonhomogeneous Markov systems with hierarchic state space working in diierent scales of time (slow and fast) that are adequate mathematical models at the analysis and modelling of various classes of computing systems and networks of a complex stochastic structure is studied. Models of asymptotic decreasing dimension and enlargement (merging) of state space are considered. Application...

This paper presents a general solution technique for discrete queueing analysis of multi-media traac on ATM in multiple dimensions, using generating function approach. The queue has multiple deterministic servers with innnite buuer size. Each server represents a time slot on an ATM link for the transmission of one cell. The arrival process is modeled by a number of independent Markov chains and...

Performance evaluation of transport layer protocols in cognitive radio sensor networks (CRSNs) is useful to provide quality-of-service for real-time reliable applications. This paper develops an analytical framework to model the steady-state sending rate of collecting cognitive radio (CR) sensors in rate-based generic additive-increase multiplicative-decrease (AIMD) and additive-increase additi...

We consider the Poisson equations for denumerable Markov chains with unbounded cost functions. Solutions to the Poisson equations exist in the Banach space of bounded real-valued functions with respect to a weighted supremum norm such that the Markov chain is geometrically ergodic. Under minor additional assumptions the solution is also unique. We give a novel probabilistic proof of this fact u...

An important fundamental problem in green communications and networking is the operation of servers (routers or base stations) with sleeping mechanism to optimize energy-delay tradeoffs. This problem is very challenging when considering realistic bursty, non-Poisson traffic. We prove for the first time the optimal structure of such a sleep mechanism for multiple servers when the arrival of jobs...

This paper presents a novel methodology for approximating the queue length (the number of customers in the system) distributions of time-varying non-Markovian manyserver queues (e.g., Gt/Gt/nt queues), where the number of servers (nt) is large. Our methodology consists of two steps. The first step uses phase-type distributions to approximate the general inter-arrival and service times, thus gen...

We consider an infinite server resequencing queue, where arrivals are generated by jumps of a semi-Markov process and service times depend on the jumps of this process. The stationary distribution of the sojourn time, conditioned on the state of the semi-Markov process, is obtained both for the case of hyperexponential service times and for the case of a Markovian arrival process. For the gener...

It has been shown by many authors that distribution properties of some characteristics in queues are inherited from those of the service times. For instances, Keilson (1978) showed that the length of a busy period in an M/G/l queue has a completely monotone density if so does the service time, Shanthikumar(1988) proved that the waiting time distribution in a GI/G/l queue is DFR if so is the ser...