865 research outputs found
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
Stochastic bounds for two-layer loss systems
This paper studies multiclass loss systems with two layers of servers, where
each server at the first layer is dedicated to a certain customer class, while
the servers at the second layer can handle all customer classes. The routing of
customers follows an overflow scheme, where arriving customers are
preferentially directed to the first layer. Stochastic comparison and coupling
techniques are developed for studying how the system is affected by packing of
customers, altered service rates, and altered server configurations. This
analysis leads to easily computable upper and lower bounds for the performance
of the system.Comment: Revised conten
Approximating multiple class queueing models with loss models
Multiple class queueing models arise in situations where some flexibility is sought through pooling of demands for different services. Earlier research has shown that most of the benefits of flexibility can be obtained with only a small proportion of cross-trained operators. Predicting the performance of a system with different types of demands and operator pools with different skills is very difficult. We present an approximation method that is based on equivalent loss systems. We successively develop approximations for the waiting probability, The average waiting time and the service level. Our approximations are validated using a series of simulations. Along the way we present some interesting insights into some similarities between queueing systems and equivalent loss systems that have to our knowledge never been reported in the literature.
Stochastic bounds for two-layer loss systems
This paper studies multiclass loss systems with two layers of servers, where each server at the first layer is dedicated to a certain customer class, while the servers at the second layer can handle all customer classes. The routing of customers follows an overflow scheme, where arriving customers are preferentially directed to the first layer. Stochastic comparison and coupling techniques are developed for studying how the system is affected by packing of customers, altered service rates, and altered server configurations. This analysis leads to easily computable upper and lower bounds for the performance of the system
Quantum correlations in dissipative gain-loss systems across exceptional points
We investigate the behavior of correlations dynamics in a dissipative
gain-loss system. First, we consider a setup made of two coupled lossy
oscillators, with one of them subject to a local gain. This provides a more
realistic platform to implement parity-time (PT) symmetry circumventing the
implementation of a pure gain. We show how the qualitative dynamics of
correlations resembles that for a pure-gain-loss setup. The major quantitative
effect is that quantum correlations are reduced, while total ones are enhanced.
Second, we study the behavior of these correlations across an exceptional point
(EP) outside of the PT-symmetric regime of parameters, observing how different
behaviors across the EP occur only in the transient dynamics. This shows how PT
symmetry plays a relevant role at large times.Comment: 6 pages, 6 figures. Submitted to the EPJST Special Issue "Recent
Advances in Collective Phenomena
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