2,578 research outputs found
Threshold queueing describes the fundamental diagram of uninterrupted traffic
Queueing due to congestion is an important aspect of road traffic. This paper provides a brief overview of queueing models for traffic and a novel threshold queue that captures the main aspects of the empirical shape of the fundamental diagram. Our numerical results characterises the sources of variation that influence the shape of the fundamental diagram
Reversibility in Queueing Models
In stochastic models for queues and their networks, random events evolve in
time. A process for their backward evolution is referred to as a time reversed
process. It is often greatly helpful to view a stochastic model from two
different time directions. In particular, if some property is unchanged under
time reversal, we may better understand that property. A concept of
reversibility is invented for this invariance. Local balance for a stationary
Markov chain has been used for a weaker version of the reversibility. However,
it is still too strong for queueing applications.
We are concerned with a continuous time Markov chain, but dose not assume it
has the stationary distribution. We define reversibility in structure as an
invariant property of a family of the set of models under certain operation.
The member of this set is a pair of transition rate function and its supporting
measure, and each set represents dynamics of queueing systems such as arrivals
and departures. We use a permutation {\Gamma} of the family menmbers, that is,
the sets themselves, to describe the change of the dynamics under time
reversal. This reversibility is is called {\Gamma}-reversibility in structure.
To apply these definitions, we introduce new classes of models, called
reacting systems and self-reacting systems. Using those definitions and models,
we give a unified view for queues and their networks which have reversibility
in structure, and show how their stationary distributions can be obtained. They
include symmetric service, batch movements and state dependent routing.Comment: Submitted for publicatio
Explicit formulas for a continuous stochastic maturation model. Application to anticancer drug pharmacokinetics/pharmacodynamics
We present a continuous time model of maturation and survival, obtained as
the limit of a compartmental evolution model when the number of compartments
tends to infinity. We establish in particular an explicit formula for the law
of the system output under inhomogeneous killing and when the input follows a
time-inhomogeneous Poisson process. This approach allows the discussion of
identifiability issues which are of difficult access for finite compartmental
models. The article ends up with an example of application for anticancer drug
pharmacokinetics/pharmacodynamics.Comment: Revised version, accepted for publication in Stochastic Models
(Taylor & Francis
Stochastic modelling of energy harvesting for low power sensor nodes
Battery lifetime is a key impediment to long-lasting low power sensor nodes. Energy or power harvesting mitigates the ependency on battery power, by converting ambient energy into electrical energy. This energy can then be used by the device for data collection and transmission. This paper proposes and analyses a queueing model to assess performance of such an energy harvesting sensor node. Accounting for energy harvesting, data collection and data transmission opportunities, the sensor node is modelled as a paired queueing system. The system has two queues, one representing accumulated energy and the other being the data queue. By means of some numerical examples, we investigate the energy-information trade-off
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Traffic signal control using queueing theory
Traffic signal control has drawn considerable attention in the literatures thanks to its ability to improve the mobility of urban networks. Queueing models are capable of capturing performance or effectiveness of a queueing system. In this report, SOCPs (second order cone program) are proposed based on different queueing models as pre-timed signal control techniques to minimize total travel delay. Stochastic programs are developed in order to handle the uncertainties in the arrival rates. In addition, the superiority of the proposed model over Webster’s model has been validated in a microscopic traffic simulation software named CORSIM.Statistic
Loss systems in a random environment
We consider a single server system with infinite waiting room in a random
environment. The service system and the environment interact in both
directions. Whenever the environment enters a prespecified subset of its state
space the service process is completely blocked: Service is interrupted and
newly arriving customers are lost. We prove an if-and-only-if-condition for a
product form steady state distribution of the joint queueing-environment
process. A consequence is a strong insensitivity property for such systems.
We discuss several applications, e.g. from inventory theory and reliability
theory, and show that our result extends and generalizes several theorems found
in the literature, e.g. of queueing-inventory processes.
We investigate further classical loss systems, where due to finite waiting
room loss of customers occurs. In connection with loss of customers due to
blocking by the environment and service interruptions new phenomena arise.
We further investigate the embedded Markov chains at departure epochs and
show that the behaviour of the embedded Markov chain is often considerably
different from that of the continuous time Markov process. This is different
from the behaviour of the standard M/G/1, where the steady state of the
embedded Markov chain and the continuous time process coincide.
For exponential queueing systems we show that there is a product form
equilibrium of the embedded Markov chain under rather general conditions. For
systems with non-exponential service times more restrictive constraints are
needed, which we prove by a counter example where the environment represents an
inventory attached to an M/D/1 queue. Such integrated queueing-inventory
systems are dealt with in the literature previously, and are revisited here in
detail
Dynamic Service Rate Control for a Single Server Queue with Markov Modulated Arrivals
We consider the problem of service rate control of a single server queueing
system with a finite-state Markov-modulated Poisson arrival process. We show
that the optimal service rate is non-decreasing in the number of customers in
the system; higher congestion rates warrant higher service rates. On the
contrary, however, we show that the optimal service rate is not necessarily
monotone in the current arrival rate. If the modulating process satisfies a
stochastic monotonicity property the monotonicity is recovered. We examine
several heuristics and show where heuristics are reasonable substitutes for the
optimal control. None of the heuristics perform well in all the regimes.
Secondly, we discuss when the Markov-modulated Poisson process with service
rate control can act as a heuristic itself to approximate the control of a
system with a periodic non-homogeneous Poisson arrival process. Not only is the
current model of interest in the control of Internet or mobile networks with
bursty traffic, but it is also useful in providing a tractable alternative for
the control of service centers with non-stationary arrival rates.Comment: 32 Pages, 7 Figure
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