Asymptotic analysis of single resource loss systems in heavy traffic, with applications to integrated networks

1995 ◽  
Vol 27 (1) ◽  
pp. 273-292 ◽  
Author(s):  
N. G. Bean ◽  
R. J. Gibbens ◽  
S. Zachary
Keyword(s):  
Asymptotic Analysis ◽  
Wide Class ◽  
Heavy Traffic ◽  
Resource Loss ◽  
Call Blocking ◽  
Integrated Networks ◽  
Asymptotic Regime ◽  
Finite Systems ◽  
Empirical Results ◽  
Loss Systems

In this paper we consider the analysis of call blocking at a single resource with differing capacity requirements as well as differing arrival rates and holding times. We include in our analysis trunk reservation parameters which provide an important mechanism for tuning the relative call blockings to desired levels. We base our work on an asymptotic regime where the resource is in heavy traffic. We further derive, from our asymptotic analysis. methods for the analysis of finite systems. Empirical results suggest that these methods perform well for a wide class of examples.

Asymptotic analysis of single resource loss systems in heavy traffic, with applications to integrated networks

1995 ◽  
Vol 27 (01) ◽  
pp. 273-292 ◽  
Author(s):  
N. G. Bean ◽  
R. J. Gibbens ◽  
S. Zachary
Keyword(s):  
Asymptotic Analysis ◽  
Wide Class ◽  
Heavy Traffic ◽  
Resource Loss ◽  
Call Blocking ◽  
Integrated Networks ◽  
Asymptotic Regime ◽  
Finite Systems ◽  
Empirical Results ◽  
Loss Systems

In this paper we consider the analysis of call blocking at a single resource with differing capacity requirements as well as differing arrival rates and holding times. We include in our analysis trunk reservation parameters which provide an important mechanism for tuning the relative call blockings to desired levels. We base our work on an asymptotic regime where the resource is in heavy traffic. We further derive, from our asymptotic analysis. methods for the analysis of finite systems. Empirical results suggest that these methods perform well for a wide class of examples.

scholarly journals Perfect sampling for infinite server and loss systems

2015 ◽  
Vol 47 (03) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Heavy Traffic ◽  
Arrival Rate ◽  
Marked Point Processes ◽  
Perfect Sampling ◽  
Running Time ◽  
Infinite Server ◽  
Loss Systems ◽  
Server System

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

ON THE NEW TRANSFORMATION-BASED APPROACH TO VALUE-AT-RISK

2008 ◽  
pp. 278-297
Author(s):  
G. P. Samanta
Keyword(s):  
Decision Making ◽  
At Risk ◽  
Normal Distribution ◽  
Financial Market ◽  
Wide Class ◽  
Value At Risk ◽  
Main Issue ◽  
Market Returns ◽  
Empirical Results ◽  
Decision Making Problem

This chapter deals with the measurement of Value-at-Risk parameter for a portfolio using historical returns. The main issue here is the estimation of suitable percentile of the underlying return distribution. If returns were normal variates, the task would have been very simple. But it is well documented in the literature that financial market returns seldom follow normal distribution. So, one has to identify suitable distribution, mostly other than normal, for the returns and find out the percentile of the identified distribution. The class of non-normal distribution, however, is extremely wide and heterogeneous, and one faces a decision-making problem of identifying the best distributional form from such a wide class of potential alternatives. In order to simplify the task of handling non-normality while estimating VaR, we adopt the transformation-based approach used in Samanta (2003). The performance of the transformation-based approach is compared with two widely used VaR models. Empirical results are quite encouraging and identify the transformation-based approach as a useful and sensible alternative.

A Fluid-Diffusion-Hybrid Limiting Approximation for Priority Systems with Fast and Slow Customers

2021 ◽  
Author(s):  
Lun Yu ◽  
Seyed Iravani ◽  
Ohad Perry
Keyword(s):  
Heavy Traffic ◽  
Priority Queue ◽  
Costs And Benefits ◽  
Fluid Limit ◽  
Asymptotically Optimal ◽  
Asymptotic Regime ◽  
Limit Process ◽  
Priority Systems ◽  
Pool System ◽  
Fluid Diffusion

The paper “Fluid-Diffusion-Hybrid (FDH) Approximation” proposes a new heavy-traffic asymptotic regime for a two-class priority system in which the high-priority customers require substantially larger service times than the low-priority customers. In the FDH limit, the high-priority queue is a diffusion, whereas the low-priority queue operates as a (random) fluid limit, whose dynamics are driven by the former diffusion. A characterizing property of our limit process is that, unlike other asymptotic regimes, a non-negligible proportion of the customers from both classes must wait for service. This property allows us to study the costs and benefits of de-pooling, and prove that a two-pool system is often the asymptotically optimal design of the system.

Asymptotic analysis of queueing systems with identical service

1996 ◽  
Vol 33 (1) ◽  
pp. 267-281 ◽  
Author(s):  
F. I. Karpelevitch ◽  
A. Ya. Kreinin
Keyword(s):  
Weak Convergence ◽  
Asymptotic Analysis ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Stationary Regime ◽  
Convergence Theory ◽  
Transient Behaviour ◽  
Limit Behaviour ◽  
Phase Systems ◽  
Multi Phase

We consider a heavy traffic regime in queueing systems with identical service. These systems belong to the class of multi-phase systems with dependent service times in different service nodes. We study the limit behaviour of the waiting time vector in heavy traffic. Both transient behaviour and the stationary regime are considered. Our analysis is based on the conception of ‘approximated functionals', which appeared to be fruitful in weak convergence theory of stochastic processes.

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