924 research outputs found
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
Modelling Pascal traffic in overflow systems
In this paper, impact of changes in parameters of offeredtraffic on the accuracy of determining the parameters of overflowtraffic in hierarchy systemswithmulti-service traffic was presented. Pascal typetrafficstreamswereoffered to the consideredsystems. The study investigated the impact of changes in the number of sources, intensity of trafficoffered by individualclasses, as well as changes in the trafficoffered by single free source. The presentedresultsarebased on determined relative errors of the values of overflowtrafficobtained in simulations and on the basis of calculations
Congestion probabilities in CDMA-based networks supporting batched Poisson traffic
We propose a new multirate teletraffic loss model for the calculation of time and call congestion probabilities in CDMA-based networks that accommodate calls of different serviceclasses whose arrival follows a batched Poisson process. The latter is more "peaked" and "bursty" than the ordinary Poisson process. The acceptance of calls in the system is based on the partial batch blocking discipline. This policy accepts a part of the batch (one or more calls) and discards the rest if the available resources are not enough to accept the whole batch. The proposed model takes into account the multiple access interference, the notion of local (soft) blocking, userâs activity and the interference cancellation. Although the analysis of the model does not lead to a product form solution of the steady state probabilities, we show that the calculation of the call-level performance metrics, time and call congestion probabilities, can be based on approximate but recursive formulas. The accuracy of the proposed formulas are verified through simulation and found to be quite satisfactory
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A Clustered Overflow Configuration of Inpatient Beds in Hospitals
Problem Definition: The shortage of inpatient beds is a major cause of delays and cancellations in many hospitals. It may also lead to patients being admitted to inappropriate wards, whereby resulting in a lower quality of care and a longer length of stay.
Academic/Practical Relevance: Investment in additional beds is not always feasible. Instead, new and creative solutions for a more efficient use of existing resources must be sought.
Methodology: We propose a new configuration of inpatient beds which we call the clustered overflow configuration. In this configuration, patients who are denied admission to their primary wards as a result of beds being fully occupied are admitted to overflow wards, with each designated to serve overflows from a certain subset of specialties and providing the same quality of care as in primary wards. We propose two different formulations for partitioning and bed allocation in the proposed configuration: one minimizing the sum of average daily costs of turning patients away and nursing teams, and another minimizing the numbers turned away subject to nursing cost falling below a given threshold. We heuristically solve instances from both formulations.
Results: Applying the models to real data shows that the configurations obtained from our models compare very well with the other configurations proposed in the literature, provided that
patients' willingness to wait is relatively short.
Managerial Implications: The proposed configuration provides the combined advantages of the dedicated configuration, wherein patients are only admitted to their primary wards, and the exible configuration, in which all specialties share a single ward. On the other hand, it restricts the adverse impacts of pooling and minimizes cross-training costs through appropriate partitioning and bed allocation. As such, it serves as a viable alternative to existing inpatient configurations
Erlang loss bounds for OT-ICU systems
In hospitals, patients can be rejected at both the operating theater (OT) and the intensive care unit (ICU) due to limited ICU capacity. The corresponding ICU rejection probability is an important service factor for hospitals. Rejection of an ICU request may lead to health deterioration for patients, and for hospitals to costly actions and a loss of precious capacity when an operation is canceled.\ud
There is no simple expression available for this ICU rejection probability that takes the interaction with the OT into account. With c the ICU capacity (number of ICU beds), this paper proves and numerically illustrates a lower bound by an system and an upper bound by an system, hence by simple Erlang loss expressions.\ud
The result is based on a product form modification for a special OTâICU tandem formulation and proved by a technically complicated Markov reward comparison approach. The upper bound result is of particular practical interest for dimensioning an ICU to secure a prespecified service quality. The numerical results include a case study.\u
Wavelength converter sharing in asynchronous optical packet/burst switching: An exact blocking analysis for markovian arrivals
Cataloged from PDF version of article.In this paper, we study the blocking probabilities
in a wavelength division multiplexing-based asynchronous
bufferless optical packet/burst switch equipped with a bank of
tuneable wavelength converters dedicated to each output fiber
line. Wavelength converter sharing, also referred to as partial
wavelength conversion, corresponds to the case of a number
of converters shared amongst a larger number of wavelength
channels. In this study, we present a probabilistic framework for
exactly calculating the packet blocking probabilities for optical
packet/burst switching systems utilizing wavelength converter
sharing. In our model, packet arrivals at the optical switch are
first assumed to be Poisson and later generalized to the more
general Markovian arrival process to cope with very general
traffic patterns whereas packet lengths are assumed to be exponentially
distributed. As opposed to the existing literature based
on approximations and/or simulations, we formulate the problem
as one of finding the steady-state solution of a continuous-time
Markov chain with a block tridiagonal infinitesimal generator. To
find such solutions, we propose a numerically efficient and stable
algorithm based on block tridiagonal LU factorizations. We show
that exact blocking probabilities can be efficiently calculated
even for very large systems and rare blocking probabilities, e.g.,
systems with 256 wavelengths per fiber and blocking probabilities
in the order of 10â40. Relying on the stability and speed of the
proposed algorithm, we also provide a means of provisioning
wavelength channels and converters in optical packet/burst
switching systems
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