1,332 research outputs found
Analysis and optimization of vacation and polling models with retrials
We study a vacation-type queueing model, and a single-server multi-queue
polling model, with the special feature of retrials. Just before the server
arrives at a station there is some deterministic glue period. Customers (both
new arrivals and retrials) arriving at the station during this glue period will
be served during the visit of the server. Customers arriving in any other
period leave immediately and will retry after an exponentially distributed
time. Our main focus is on queue length analysis, both at embedded time points
(beginnings of glue periods, visit periods and switch- or vacation periods) and
at arbitrary time points.Comment: Keywords: vacation queue, polling model, retrials Submitted for
review to Performance evaluation journal, as an extended version of 'Vacation
and polling models with retrials', by Onno Boxma and Jacques Resin
The 13C nuclear magnetic resonance in graphite intercalation compounds
The (13)C NMR chemical shifts of graphite intercalation compounds were calculated. For acceptor types, the shifts come mainly from the paramagnetic (Ramsey) intra-atomic terms. They are related to the gross features of the two-dimensional band structures. The calculated anisotropy is about -140 ppm and is independent of the finer details such as charge transfer. For donor types, the carbon 2p pi orbitals are spin-polarized because of mixing with metal conduction electrons, thus there is an additional dipolar contribution which may be correlated with the electronic specific heat. The general agreement with experimental data is satisfactory
Heavy traffic analysis of a polling model with retrials and glue periods
We present a heavy traffic analysis of a single-server polling model, with
the special features of retrials and glue periods. The combination of these
features in a polling model typically occurs in certain optical networking
models, and in models where customers have a reservation period just before
their service period. Just before the server arrives at a station there is some
deterministic glue period. Customers (both new arrivals and retrials) arriving
at the station during this glue period will be served during the visit of the
server. Customers arriving in any other period leave immediately and will retry
after an exponentially distributed time. As this model defies a closed-form
expression for the queue length distributions, our main focus is on their
heavy-traffic asymptotics, both at embedded time points (beginnings of glue
periods, visit periods and switch periods) and at arbitrary time points. We
obtain closed-form expressions for the limiting scaled joint queue length
distribution in heavy traffic and use these to accurately approximate the mean
number of customers in the system under different loads.Comment: 23 pages, 2 figure
Condition-based maintenance at both scheduled and unscheduled opportunities
Motivated by original equipment manufacturer (OEM) service and maintenance
practices we consider a single component subject to replacements at failure
instances and two types of preventive maintenance opportunities: scheduled,
which occur due to periodic system reviews of the equipment, and unscheduled,
which occur due to failures of other components in the system. Modelling the
state of the component appropriately and incorporating a realistic cost
structure for corrective maintenance as well as condition-based maintenance
(CBM), we derive the optimal CBM policy. In particular, we show that the
optimal long-run average cost policy for the model at hand is a control-limit
policy, where the control limit depends on the time until the next scheduled
opportunity. Furthermore, we explicitly calculate the long-run average cost for
any given control-limit time dependent policy and compare various policies
numerically.Comment: published at proceedings of the 9th IMA International Conference on
Modelling in Industrial Maintenance and Reliability (MIMAR), 201
Optimizing the Throughput of Particulate Streams Subject to Blocking
Filtration, flow in narrow channels and traffic flow are examples of
processes subject to blocking when the channel conveying the particles becomes
too crowded. If the blockage is temporary, which means that after a finite time
the channel is flushed and reopened, one expects to observe a maximum
throughput for a finite intensity of entering particles. We investigate this
phenomenon by introducing a queueing theory inspired, circular Markov model.
Particles enter a channel with intensity and exit at a rate . If
particles are present at the same time in the channel, the system becomes
blocked and no more particles can enter until the blockage is cleared after an
exponentially distributed time with rate . We obtain an exact expression
for the steady state throughput (including the exiting blocked particles) for
all values of . For we show that the throughput assumes a maximum
value for finite if . The time-dependent throughput
either monotonically approaches the steady state value, or reaches a maximum
value at finite time. We demonstrate that, in the steady state, this model can
be mapped to a previously introduced non-Markovian model with fixed transit and
blockage times.
We also examine an irreversible, non-Markovian blockage process with constant
transit time exposed to an entering flux of fixed intensity for a finite time
and we show that the first and second moments of the number of exiting
particles are maximized for a finite intensity.Comment: 20 pages, 13 figure
Two parallel insurance lines with simultaneous arrivals and risks correlated with inter-arrival times
We investigate an insurance risk model that consists of two reserves which
receive income at fixed rates. Claims are being requested at random epochs from
each reserve and the interclaim times are generally distributed. The two
reserves are coupled in the sense that at a claim arrival epoch, claims are
being requested from both reserves and the amounts requested are correlated. In
addition, the claim amounts are correlated with the time elapsed since the
previous claim arrival. We focus on the probability that this bivariate reserve
process survives indefinitely. The infinite- horizon survival problem is shown
to be related to the problem of determining the equilibrium distribution of a
random walk with vector-valued increments with reflecting boundary. This
reflected random walk is actually the waiting time process in a queueing system
dual to the bivariate ruin process. Under assumptions on the arrival process
and the claim amounts, and using Wiener-Hopf factor- ization with one
parameter, we explicitly determine the Laplace-Stieltjes transform of the
survival function, c.q., the two-dimensional equilibrium waiting time
distribution. Finally, the bivariate transforms are evaluated for some
examples, including for proportional reinsurance, and the bivariate ruin
functions are numerically calculated using an efficient inversion scheme.Comment: 24 pages, 6 figure
Queues and risk processes with dependencies
We study the generalization of the G/G/1 queue obtained by relaxing the
assumption of independence between inter-arrival times and service
requirements. The analysis is carried out for the class of multivariate matrix
exponential distributions introduced in [12]. In this setting, we obtain the
steady state waiting time distribution and we show that the classical relation
between the steady state waiting time and the workload distributions re- mains
valid when the independence assumption is relaxed. We also prove duality
results with the ruin functions in an ordinary and a delayed ruin process.
These extend several known dualities between queueing and risk models in the
independent case. Finally we show that there exist stochastic order relations
between the waiting times under various instances of correlation
Mine Countermeasures in Coastal Harbors: A Force Planner\u27s Dilemma
Much has been written about the power projection and sea control functions of the 600-ship navy; yet a small but vitally important aspect of accomplishing this strategy is largely ignored by force planners. The naval mine, as an offensive weapon used against U.S. ports and harbors, could have a disastrous effect on the timely execution of a maritime strategy
Revenue Maximization in an Optical Router Node Using Multiple Wavelengths
In this paper, an optical router node with multiple wavelengths is
considered. We introduce revenue for successful transmission and study the
ensuing revenue maximization problem. We present an efficient and accurate
heuristic procedure for solving the NP-hard revenue maximization problem and
investigate the advantage offered by having multiple wavelengths
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