For a Markov-modulated random walk with negative drift and long-tailed right tail we prove that the ascending ladder height matrix distribution is asymptotically proportional to a long-tailed distribution. This result enable us to generalize a recent result on subexponential asymptotics of a Markov-modulated M/G/1 queue to subexponential asymptotics of a Markov-modulated G/G/1 queue. For a clas...

Many real-life systems can be modeled using the classical M/G/c/N queue. A frequently-used approach is to replace the general service time distribution by a phase-type distribution since the M/Ph/c/N queue can be described by familiar balance equations. The downside of this approach is that the size of the resulting state space suffers from the “dimensionality curse”, i.e., exhibits combinatori...

We describe a scalable priority queue manager that implements deadline-ordered service disciplines in an output-buffered ATM switch, which can be used as a switching node in high-speed packet switched networks to provide quality of service (QoS) guarantees. The priority queue manager can handle a range of priority levels from to , a buffer size of 64K ATM cells, and 16 input links at 2.5 Gb/s. ...

In this paper a single server preemptive priority queuing system consisting of two types of customer units with Poisson arrival, exponential service time distribution and exponential vacation is analyzed. Two type of customer units of which higher priority units of unlimited Poisson input are served by bulk service rule and limited Poisson input of low priority units served singly. The bulk ser...

M=G=1 non-preemptive priority queue with bulk arrivals has already been analysed in many papers. Two problems are known in this area: first, when the number of priorities is greater than 2, the analysis for priority processes is obviously very difficult to handle. Therefore, the earlier work on the subject was restricted mostly to two priority classes; and second, although analytically explicit...

Abstract Here a two-state batch arrivals and batch service Markovian queue with server vacation model has been taken into consideration for its mathematical modelling and performance analysis under transient state. The present Markovian queueing model considers a single server with multiple vacations and both arrivals and services in batches of variable size. Arriving customers are processed by...

In this paper, we study the performance of packet concentrators with input queueing. A recent concentrator model given by Gündüzhan and Oruç considers packet concentrators with different input and output packet rates and gives a minimum crosspoint complexity construction for buffered sparse crossbar concentrators. We use this model as a basis for the performance evaluation of concentrators whic...

In this paper we describe G/G/R+s multi- repairmen machining system with balking. The system consists of M operating machines, S spare machines, R permanent and s additional repairmen. Assuming the discrete flow of machines by continuous one, the diffusion approximation technique for the machine repair system has developed. The system will be in normal working mode if there is M operating machi...