2,976 research outputs found
Coupled queues with customer impatience
Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved
Perturbation Analysis of a Variable M/M/1 Queue: A Probabilistic Approach
Motivated by the problem of the coexistence on transmission links of
telecommunication networks of elastic and unresponsive traffic, we study in
this paper the impact on the busy period of an M/M/1 queue of a small
perturbation in the server rate. The perturbation depends upon an independent
stationary process (X(t)) and is quantified by means of a parameter \eps \ll 1.
We specifically compute the two first terms of the power series expansion in
\eps of the mean value of the busy period duration. This allows us to study the
validity of the Reduced Service Rate (RSR) approximation, which consists in
comparing the perturbed M/M/1 queue with the M/M/1 queue where the service rate
is constant and equal to the mean value of the perturbation. For the first term
of the expansion, the two systems are equivalent. For the second term, the
situation is more complex and it is shown that the correlations of the
environment process (X(t)) play a key role
The effective bandwidth problem revisited
The paper studies a single-server queueing system with autonomous service and
priority classes. Arrival and departure processes are governed by marked
point processes. There are buffers corresponding to priority classes,
and upon arrival a unit of the th priority class occupies a place in the
th buffer. Let , denote the quota for the total
th buffer content. The values are assumed to be large, and
queueing systems both with finite and infinite buffers are studied. In the case
of a system with finite buffers, the values characterize buffer
capacities.
The paper discusses a circle of problems related to optimization of
performance measures associated with overflowing the quota of buffer contents
in particular buffers models. Our approach to this problem is new, and the
presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in
Stochastic Model
A Maclaurin-series expansion approach to coupled queues with phase-type distributed service times
International audienc
Capacity and Stable Scheduling in Heterogeneous Wireless Networks
Heterogeneous wireless networks (HetNets) provide a means to increase network
capacity by introducing small cells and adopting a layered architecture.
HetNets allocate resources flexibly through time sharing and cell range
expansion/contraction allowing a wide range of possible schedulers. In this
paper we define the capacity of a HetNet down link in terms of the maximum
number of downloads per second which can be achieved for a given offered
traffic density. Given this definition we show that the capacity is determined
via the solution to a continuous linear program (LP). If the solution is
smaller than 1 then there is a scheduler such that the number of mobiles in the
network has ergodic properties with finite mean waiting time. If the solution
is greater than 1 then no such scheduler exists. The above results continue to
hold if a more general class of schedulers is considered.Comment: 30 pages, 6 figure
On Spectral Properties of Finite Population Processor Shared Queues
We consider sojourn or response times in processor-shared queues that have a
finite population of potential users. Computing the response time of a tagged
customer involves solving a finite system of linear ODEs. Writing the system in
matrix form, we study the eigenvectors and eigenvalues in the limit as the size
of the matrix becomes large. This corresponds to finite population models where
the total population is . Using asymptotic methods we reduce the
eigenvalue problem to that of a standard differential equation, such as the
Hermite equation. The dominant eigenvalue leads to the tail of a customer's
sojourn time distribution.Comment: 28 pages, 7 figures and 5 table
- …