25 research outputs found
EUROPEAN CONFERENCE ON QUEUEING THEORY 2016
International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"
Error bounds for last-column-block-augmented truncations of block-structured Markov chains
This paper discusses the error estimation of the last-column-block-augmented
northwest-corner truncation (LC-block-augmented truncation, for short) of
block-structured Markov chains (BSMCs) in continuous time. We first derive
upper bounds for the absolute difference between the time-averaged functionals
of a BSMC and its LC-block-augmented truncation, under the assumption that the
BSMC satisfies the general -modulated drift condition. We then establish
computable bounds for a special case where the BSMC is exponentially ergodic.
To derive such computable bounds for the general case, we propose a method that
reduces BSMCs to be exponentially ergodic. We also apply the obtained bounds to
level-dependent quasi-birth-and-death processes (LD-QBDs), and discuss the
properties of the bounds through the numerical results on an M/M/ retrial
queue, which is a representative example of LD-QBDs. Finally, we present
computable perturbation bounds for the stationary distribution vectors of
BSMCs.Comment: This version has fixed the bugs for the positions of Figures 1
through
A retrial system with two input streams and two orbit queues
Two independent Poisson streams of jobs flow into a single-server service
system having a limited common buffer that can hold at most one job. If a
type-i job (i=1,2) finds the server busy, it is blocked and routed to a
separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at
its specific Poisson rate. This creates a system with three dependent queues.
Such a queueing system serves as a model for two competing job streams in a
carrier sensing multiple access system. We study the queueing system using
multi-dimensional probability generating functions, and derive its necessary
and sufficient stability conditions while solving a boundary value problem.
Various performance measures are calculated and numerical results are
presented.Comment: N° RR-7999 (2012
A Multi-Server Retrial Queueing Inventory System With Asynchronous Multiple Vacations
This article deals with asynchronous server vacation and customer retrial
facility in a multi-server queueing-inventory system. The Poisson process
governs the arrival of a customer. The system is comprised of c identical
servers, a finite-size waiting area, and a storage area containing S items. The
service time is distributed exponentially. If each server finds that there are
an insufficient number of customers and items in the system after the busy
period, they start a vacation. Once the servers vacation is over and it
recognizes there is no chance of getting busy, it goes into an idle state if
the number of customers or items is not sufficient, otherwise, it will take
another vacation. Furthermore, each server's vacation period occurs
independently of the other servers. The system accepts a (s, Q) control policy
for inventory replenishment. For the steady state analysis, the Marcel F Neuts
and B Madhu Rao matrix geometric approximation approach is used owing to the
structure of an infinitesimal generator matrix. The necessary stability
condition and R matrix are to be computed and presented. After calculating the
sufficient system performance measures, an expected total cost of the system is
to be constructed and numerically incorporated with the parameters.
Additionally, numerical analyses will be conducted to examine the waiting time
of customers in the queue and in orbit, as well as the expected rate of
customer loss.Comment: 43 pages, 12 figures, 5 table