Consecutive customer loss probabilities in M/G/1/n and GI/M(m)//n systems

2006 ◽  
Author(s):  
António Pacheco ◽  
Helena Ribeiro
Keyword(s):  
Loss Probabilities

scholarly journals A queueing model for error control of partial buffer sharing in ATM

1999 ◽  
Vol 5 (4) ◽  
pp. 329-348
Author(s):  
Boo Yong Ahn ◽  
Ho Woo Lee
Keyword(s):  
Error Control ◽  
Approximation Scheme ◽  
Queueing System ◽  
Recursive Method ◽  
Loss Probabilities ◽  
Mean Waiting Time ◽  
System Equations ◽  
The Mean ◽  
Buffer Sharing

We model the error control of the partial buffer sharing of ATM by a queueing systemM1,M2/G/1/K+1with threshold and instantaneous Bernoulli feedback. We first derive the system equations and develop a recursive method to compute the loss probabilities at an arbitrary time epoch. We then build an approximation scheme to compute the mean waiting time of each class of cells. An algorithm is developed for finding the optimal threshold and queue capacity for a given quality of service.

scholarly journals Tight Upper Bounds for Cell Loss Probabilities and Required Bandwidth Estimation in ATM Multiplexers

1999 ◽  
Vol 10 (1) ◽  
pp. 33-43
Author(s):  
Lru Xiaoming ◽  
Liu Liming ◽  
Brahim Bensaou ◽  
Danny H. K. Tsang
Keyword(s):  
Cell Loss ◽  
Upper Bounds ◽  
Bandwidth Estimation ◽  
Loss Probabilities

Loss probabilities in a simple circuit-switched network

1994 ◽  
Vol 26 (2) ◽  
pp. 456-473 ◽  
Author(s):  
J. A. Morrison
Keyword(s):  
Fixed Point ◽  
Parameter Space ◽  
Asynchronous Transfer Mode ◽  
Practical Interest ◽  
Integral Representations ◽  
Cellular Systems ◽  
Holding Period ◽  
Loss Probabilities ◽  
Erlang Loss ◽  
Exponentially Small

In this paper a particular loss network consisting of two links with C1 and C2 circuits, respectively, and two fixed routes, is investigated. A call on route 1 uses a circuit from both links, and a call on route 2 uses a circuit from only the second link. Calls requesting routes 1 and 2 arrive as independent Poisson streams. A call requesting route 1 is blocked and lost if there are no free circuits on either link, and a call requesting route 2 is blocked and lost if there is no free circuit on the second link. Otherwise the call is connected and holds a circuit from each link on its route for the holding period of the call.The case in which the capacities C1, and C2, and the traffic intensities v1, and v2, all become large of O(N) where N » 1, but with their ratios fixed, is considered. The loss probabilities L1 and L2 for calls requesting routes 1 and 2, respectively, are investigated. The asymptotic behavior of L1 and L2 as N→ ∞ is determined with the help of double contour integral representations and saddlepoint approximations. The results differ in various regions of the parameter space (C1, C2, v1, v2). In some of these results the loss probabilities are given in terms of the Erlang loss function, with appropriate arguments, to within an exponentially small relative error. The results provide new information when the loss probabilities are exponentially small in N. This situation is of practical interest, e.g. in cellular systems, and in asynchronous transfer mode networks, where very small loss probabilities are desired.The accuracy of the Erlang fixed-point approximations to the loss probabilities is also investigated. In particular, it is shown that the fixed-point approximation E2 to L2 is inaccurate in a certain region of the parameter space, since L2 « E2 there. On the other hand, in some regions of the parameter space the fixed-point approximations to both L1 and L2 are accurate to within an exponentially small relative error.

Cell loss asymptotics for buffers fed with a large number of independent stationary sources

1999 ◽  
Vol 36 (1) ◽  
pp. 86-96 ◽  
Author(s):  
Nikolay Likhanov ◽  
Ravi R. Mazumdar
Keyword(s):  
Local Limit ◽  
Cell Loss ◽  
Buffer Overflow ◽  
Finite Buffer ◽  
Loss Probabilities ◽  
Measure Change ◽  
Self Similar ◽  
Heavy Tailed ◽  
Overflow Probabilities ◽  
Stationary Sources

In this paper we derive asymptotically exact expressions for buffer overflow probabilities and cell loss probabilities for a finite buffer which is fed by a large number of independent and stationary sources. The technique is based on scaling, measure change and local limit theorems and extends the recent results of Courcoubetis and Weber on buffer overflow asymptotics. We discuss the cases when the buffers are of the same order as the transmission bandwidth as well as the case of small buffers. Moreover we show that the results hold for a wide variety of traffic sources including ON/OFF sources with heavy-tailed distributed ON periods, which are typical candidates for so-called ‘self-similar’ inputs, showing that the asymptotic cell loss probability behaves in much the same manner for such sources as for the Markovian type of sources, which has important implications for statistical multiplexing. Numerical validation of the results against simulations are also reported.

Surface loss probabilities of H and N radicals on different materials in afterglow plasmas employing H2 and N2 mixture gases

2010 ◽  
Vol 107 (10) ◽  
pp. 103310 ◽  
Author(s):  
Chang Sung Moon ◽  
Keigo Takeda ◽  
Seigo Takashima ◽  
Makoto Sekine ◽  
Yuichi Setsuhara ◽  
...  
Keyword(s):  
Surface Loss ◽  
Loss Probabilities
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