Clustering clinical departments for wards to achieve a prespecified blocking probability

When the number of available beds in a hospital is limited and fixed, it can be beneficial to cluster several clinical departments such that the probability of not being able to admit a patient is acceptably small. The clusters are then assigned to the available wards such that enough beds are available to guarantee a blocking probability below a prespecified value. We first give an exact formulation of the problem to be able to achieve optimal solutions. To reduce computation times, we also introduce two heuristic solution methods. The first heuristic is similar to the exact solution method, however, the number of beds needed is approximated by a linear function. The second heuristic uses a local search approach to determine the assignment of clinical departments to clusters and a restricted version of the exact solution method to determine the assignment of clusters to wards

Approximations for time-dependent distributions in Markovian fluid models

In this paper we study the distribution of the level at time $\theta$ of Markovian fluid queues and Markovian continuous time random walks, the maximum (and minimum) level over $[0,\theta]$, and their joint distributions. We approximate $\theta$ by a random variable $T$ with Erlang distribution and we use an alternative way, with respect to the usual Laplace transform approach, to compute the distributions. We present probabilistic interpretation of the equations and provide a numerical illustration

Analysis and implementation of the Large Scale Video-on-Demand System

Next Generation Network (NGN) provides multimedia services over broadband based networks, which supports high definition TV (HDTV), and DVD quality video-on-demand content. The video services are thus seen as merging mainly three areas such as computing, communication, and broadcasting. It has numerous advantages and more exploration for the large-scale deployment of video-on-demand system is still needed. This is due to its economic and design constraints. It's need significant initial investments for full service provision. This paper presents different estimation for the different topologies and it require efficient planning for a VOD system network. The methodology investigates the network bandwidth requirements of a VOD system based on centralized servers, and distributed local proxies. Network traffic models are developed to evaluate the VOD system's operational bandwidth requirements for these two network architectures. This paper present an efficient estimation of the of the bandwidth requirement for the different architectures.Comment: 9 pages, 8 figure

A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times

In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as \emph{supermarket models}) with phase-type (PH) service times. Generalizing the service times to the phase-type distribution makes the analysis of the supermarket models more difficult and challenging than that of the exponential service time case which has been extensively discussed in the literature. We first describe the supermarket model as a system of differential vector equations, and provide a doubly exponential solution to the fixed point of the system of differential vector equations. Then we analyze the exponential convergence of the current location of the supermarket model to its fixed point. Finally, we present numerical examples to illustrate our approach and show its effectiveness in analyzing the randomized load balancing schemes with non-exponential service requirements.Comment: 24 page

Stability Analysis of GI/G/c/K Retrial Queue with Constant Retrial Rate

We consider a GI/G/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has $c$ identical servers and can accommodate the maximal number of $K$ jobs. If a newly arriving job finds the full primary queue, it joins the orbit. The original primary jobs arrive to the system according to a renewal process. The jobs have general i.i.d. service times. A job in front of the orbit queue retries to enter the primary queue after an exponentially distributed time independent of the orbit queue length. Telephone exchange systems, Medium Access Protocols and short TCP transfers are just some applications of the proposed queueing system. For this system we establish minimal sufficient stability conditions. Our model is very general. In addition, to the known particular cases (e.g., M/G/1/1 or M/M/c/c systems), the proposed model covers as particular cases the deterministic service model and the Erlang model with constant retrial rate. The latter particular cases have not been considered in the past. The obtained stability conditions have clear probabilistic interpretation