4,259 research outputs found
Delay analysis of a two-class batch-service queue with class-dependent variable server capacity
In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length of a sequence of same-class customers. This type of batch server can be found in telecommunications systems and production environments. We first determine the steady state partial probability generating function of the queue occupancy at customer arrival epochs. Using a spectral decomposition technique, we obtain the steady state probability generating function of the delay of a random customer. We also show that the distribution of the delay of a random customer corresponds to a phase-type distribution. Finally, some numerical examples are given that provide further insight in the impact of asymmetry and variance in the arrival process on the number of customers in the system and the delay of a random customer
Analysis and Computation of the Joint Queue Length Distribution in a FIFO Single-Server Queue with Multiple Batch Markovian Arrival Streams
This paper considers a work-conserving FIFO single-server queue with multiple
batch Markovian arrival streams governed by a continuous-time finite-state
Markov chain. A particular feature of this queue is that service time
distributions of customers may be different for different arrival streams.
After briefly discussing the actual waiting time distributions of customers
from respective arrival streams, we derive a formula for the vector generating
function of the time-average joint queue length distribution in terms of the
virtual waiting time distribution. Further assuming the discrete phase-type
batch size distributions, we develop a numerically feasible procedure to
compute the joint queue length distribution. Some numerical examples are
provided also
Modeling, Analysis and Impact of a Long Transitory Phase in Random Access Protocols
In random access protocols, the service rate depends on the number of
stations with a packet buffered for transmission. We demonstrate via numerical
analysis that this state-dependent rate along with the consideration of Poisson
traffic and infinite (or large enough to be considered infinite) buffer size
may cause a high-throughput and extremely long (in the order of hours)
transitory phase when traffic arrivals are right above the stability limit. We
also perform an experimental evaluation to provide further insight into the
characterisation of this transitory phase of the network by analysing
statistical properties of its duration. The identification of the presence as
well as the characterisation of this behaviour is crucial to avoid
misprediction, which has a significant potential impact on network performance
and optimisation. Furthermore, we discuss practical implications of this
finding and propose a distributed and low-complexity mechanism to keep the
network operating in the high-throughput phase.Comment: 13 pages, 10 figures, Submitted to IEEE/ACM Transactions on
Networkin
Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times
Queueing models with batch service have been studied frequently, for instance in the domain of telecommunications or manufacturing. Although the batch server's capacity may be variable in practice, only a few authors have included variable capacity in their models. We analyse a batch server with multiple customer classes and a variable service capacity that depends on both the number of waiting customers and their classes. The service times are generally distributed and class-dependent. These features complicate the analysis in a non-trivial way. We tackle it by examining the system state at embedded points, and studying the resulting Markov Chain.
We first establish the joint probability generating function (pgf) of the service capacity and the number of customers left behind in the queue immediately after service initiation epochs. From this joint pgf, we extract the pgf for the number of customers in the queue and in the system respectively at service initiation epochs and departure epochs, and the pgf of the actual server capacity. Combined with additional techniques, we also obtain the pgf of the queue and system content at customer arrival epochs and random slot boundaries, and the pgf of the delay of a random customer. In the numerical experiments, we focus on the impact of correlation between the classes of consecutive customers, and on the influence of different service time distributions on the system performance. (C) 2019 Elsevier B.V. All rights reserved
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