1,472 research outputs found
Estimating customer impatience in a service system with unobserved balking
This paper studies a service system in which arriving customers are provided
with information about the delay they will experience. Based on this
information they decide to wait for service or to leave the system. The main
objective is to estimate the customers' patience-level distribution and the
corresponding potential arrival rate, using knowledge of the actual
queue-length process only. The main complication, and distinguishing feature of
our setup, lies in the fact that customers who decide not to join are not
observed, but, remarkably, we manage to devise a procedure to estimate the load
they would generate. We express our system in terms of a multi-server queue
with a Poisson stream of customers, which allows us to evaluate the
corresponding likelihood function. Estimating the unknown parameters relying on
a maximum likelihood procedure, we prove strong consistency and derive the
asymptotic distribution of the estimation error. Several applications and
extensions of the method are discussed. The performance of our approach is
further assessed through a series of numerical experiments. By fitting
parameters of hyperexponential and generalized-hyperexponential distributions
our method provides a robust estimation framework for any continuous
patience-level distribution
Approximations and Bounds for (n, k) Fork-Join Queues: A Linear Transformation Approach
Compared to basic fork-join queues, a job in (n, k) fork-join queues only
needs its k out of all n sub-tasks to be finished. Since (n, k) fork-join
queues are prevalent in popular distributed systems, erasure coding based cloud
storages, and modern network protocols like multipath routing, estimating the
sojourn time of such queues is thus critical for the performance measurement
and resource plan of computer clusters. However, the estimating keeps to be a
well-known open challenge for years, and only rough bounds for a limited range
of load factors have been given. In this paper, we developed a closed-form
linear transformation technique for jointly-identical random variables: An
order statistic can be represented by a linear combination of maxima. This
brand-new technique is then used to transform the sojourn time of non-purging
(n, k) fork-join queues into a linear combination of the sojourn times of basic
(k, k), (k+1, k+1), ..., (n, n) fork-join queues. Consequently, existing
approximations for basic fork-join queues can be bridged to the approximations
for non-purging (n, k) fork-join queues. The uncovered approximations are then
used to improve the upper bounds for purging (n, k) fork-join queues.
Simulation experiments show that this linear transformation approach is
practiced well for moderate n and relatively large k.Comment: 10 page
Heavy Traffic Limit for a Tandem Queue with Identical Service Times
We consider a two-node tandem queueing network in which the upstream queue is
M/G/1 and each job reuses its upstream service requirement when moving to the
downstream queue. Both servers employ the first-in-first-out policy. We
investigate the amount of work in the second queue at certain embedded arrival
time points, namely when the upstream queue has just emptied. We focus on the
case of infinite-variance service times and obtain a heavy traffic process
limit for the embedded Markov chain
Need a Lift? An Elevator Queueing Problem
Various aspects of the behavior and dispatching of elevators (lifts) were studied. Monte Carlo simulation was used to study the statistics of the several models for the peak demand at uppeak times. Analytical models problems were used to prove or disprove whether schemes were optimal. A mostly integer programming problem was formulated but not studied further
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