Server utilization factors in queueing loss systems with ordered entry and heterogeneous servers

1986 ◽  
Vol 23 (01) ◽  
pp. 236-242 ◽  
Author(s):  
Behnam Pourbabai ◽  
David Sonderman
Keyword(s):  
Simulation Study ◽  
Approximation Method ◽  
Counting Process ◽  
Numerical Results ◽  
Heterogeneous Servers ◽  
Loss System ◽  
Utilization Factor ◽  
Service Rates ◽  
Loss Systems ◽  
Server Utilization

Approximation expressions for the server utilization factor of each server in a heterogeneous-server G/G/n queueing loss system with ordered entry are derived. The system is assumed to face a stationary counting process. Service times are generally distributed with possibly different service rates. The numerical results from this approximation method are then compared with those from a simulation study.

Server utilization factors in queueing loss systems with ordered entry and heterogeneous servers

1986 ◽  
Vol 23 (1) ◽  
pp. 236-242 ◽  
Author(s):  
Behnam Pourbabai ◽  
David Sonderman
Keyword(s):  
Simulation Study ◽  
Approximation Method ◽  
Counting Process ◽  
Numerical Results ◽  
Heterogeneous Servers ◽  
Loss System ◽  
Utilization Factor ◽  
Service Rates ◽  
Loss Systems ◽  
Server Utilization

Approximation expressions for the server utilization factor of each server in a heterogeneous-server G/G/n queueing loss system with ordered entry are derived. The system is assumed to face a stationary counting process. Service times are generally distributed with possibly different service rates. The numerical results from this approximation method are then compared with those from a simulation study.

Optimal service rates in the multiserver loss system with heterogeneous servers

1981 ◽  
Vol 18 (03) ◽  
pp. 776-781 ◽  
Author(s):  
G. B. Nath ◽  
E. G. Enns
Keyword(s):  
Heterogeneous System ◽  
Percentage Reduction ◽  
Heterogeneous Servers ◽  
Loss System ◽  
Optimal Service ◽  
Service Rates

A multichannel loss system with heterogeneous servers operating in parallel is analyzed. The sum of the service rates of all servers is assumed constant. The optimal service rates that minimize the probability of losing a customer are obtained, and are shown to be different from each other. The percentage reduction in the probability of losing a customer in the homogeneous and the best heterogeneous system for a few representative values are included.

A note on a D/G/K loss system with retrials

1990 ◽  
Vol 27 (2) ◽  
pp. 385-392 ◽  
Author(s):  
Behnam Pourbabai
Keyword(s):  
Steady State ◽  
Processing Time ◽  
Distributed Processing ◽  
Random Access ◽  
Heterogeneous Servers ◽  
Loss System ◽  
System A ◽  
Loss Systems

An algorithm is suggested for approximating the performance of a D/G/K loss system with deterministic input, generally distributed processing time, K heterogeneous servers, the random access processing discipline, and retrials in steady state. In loss systems with retrials, the units which at the instants of their arrival at the system find all the servers busy, are not lost: those units retry to be processed by merging with the incoming arrival units. In this system, a fraction of the units which have not initially been processed will be allowed to leave the system. The performance of this system in steady state is approximated by a recursive technique.

A note on a D/G/K loss system with retrials

1990 ◽  
Vol 27 (02) ◽  
pp. 385-392
Author(s):  
Behnam Pourbabai
Keyword(s):  
Steady State ◽  
Processing Time ◽  
Distributed Processing ◽  
Random Access ◽  
Heterogeneous Servers ◽  
Loss System ◽  
System A ◽  
Loss Systems

An algorithm is suggested for approximating the performance of a D/G/K loss system with deterministic input, generally distributed processing time, K heterogeneous servers, the random access processing discipline, and retrials in steady state. In loss systems with retrials, the units which at the instants of their arrival at the system find all the servers busy, are not lost: those units retry to be processed by merging with the incoming arrival units. In this system, a fraction of the units which have not initially been processed will be allowed to leave the system. The performance of this system in steady state is approximated by a recursive technique.

Optimal service rates in the multiserver loss system with heterogeneous servers

1981 ◽  
Vol 18 (3) ◽  
pp. 776-781 ◽  
Author(s):  
G. B. Nath ◽  
E. G. Enns
Keyword(s):  
Heterogeneous System ◽  
Percentage Reduction ◽  
Heterogeneous Servers ◽  
Loss System ◽  
Optimal Service ◽  
Service Rates

A multichannel loss system with heterogeneous servers operating in parallel is analyzed. The sum of the service rates of all servers is assumed constant. The optimal service rates that minimize the probability of losing a customer are obtained, and are shown to be different from each other. The percentage reduction in the probability of losing a customer in the homogeneous and the best heterogeneous system for a few representative values are included.

scholarly journals Robust scheduling for flexible processing networks

2017 ◽  
Vol 49 (2) ◽  
pp. 603-628 ◽  
Author(s):  
Ramtin Pedarsani ◽  
Jean Walrand ◽  
Yuan Zhong
Keyword(s):  
Queueing Networks ◽  
Complex Structure ◽  
Job Flows ◽  
Heterogeneous Servers ◽  
Robust Scheduling ◽  
System Parameters ◽  
Balanced Allocation ◽  
Service Rates ◽  
Length Changes ◽  
Processing Networks

Abstract Modern processing networks often consist of heterogeneous servers with widely varying capabilities, and process job flows with complex structure and requirements. A major challenge in designing efficient scheduling policies in these networks is the lack of reliable estimates of system parameters, and an attractive approach for addressing this challenge is to design robust policies, i.e. policies that do not use system parameters such as arrival and/or service rates for making scheduling decisions. In this paper we propose a general framework for the design of robust policies. The main technical novelty is the use of a stochastic gradient projection method that reacts to queue-length changes in order to find a balanced allocation of service resources to incoming tasks. We illustrate our approach on two broad classes of processing systems, namely the flexible fork-join networks and the flexible queueing networks, and prove the rate stability of our proposed policies for these networks under nonrestrictive assumptions.

scholarly journals The distribution of wasted spaces in the M/M/∞ queue with ranked servers

2008 ◽  
Vol 40 (03) ◽  
pp. 835-855 ◽  
Author(s):  
Eunju Sohn ◽  
Charles Knessl
Keyword(s):  
Probability Distribution ◽  
Numerical Results ◽  
Tail Behavior ◽  
Service Rates ◽  
The Difference

We consider the M/M/∞ queue with m primary servers and infinitely many secondary servers. All the servers are numbered and ordered. An arriving customer takes the lowest available server. We define the wasted spaces as the difference between the highest numbered occupied server and the total number of occupied servers. Letting ρ = λ0/μ be the ratio of arrival to service rates, we study the probability distribution of the wasted spaces asymptotically for ρ → ∞. We also give some numerical results and the tail behavior for ρ = O(1).

scholarly journals Application of the successive approximation method to the analysis of bending plates

2018 ◽  
Vol 251 ◽  
pp. 04058
Author(s):  
Radek Gabbasov ◽  
Vladimir Filatov ◽  
Nikita Ryasny
Keyword(s):  
Boundary Conditions ◽  
Successive Approximation ◽  
Approximation Method ◽  
High Accuracy ◽  
Numerical Results ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Successive Approximation Method ◽  
Medium Thickness ◽  
Bending Plates

This work presents an algorithm for calculating the bending plates of medium thickness according to the Reissner’. To obtain numerical results, the method of successive approximations (MSA) is used. This method has high accuracy and fast convergence, which was confirmed by the solution of a range of tasks. Publication of the results of the calculation of plates of medium thickness with the boundary conditions revised here is supposed to be in the following articles.

scholarly journals A Simple Approximation Method for Obtaining the Spanwise Lift Distribution

1941 ◽  
Vol 45 (370) ◽  
pp. 331-336 ◽  
Author(s):  
O. Schrenk
Keyword(s):  
Approximation Method ◽  
Numerical Results ◽  
Exact Method ◽  
Simple Approximation ◽  
Satisfactory Degree ◽  
Computation Work

In this paper a simple approximation method is presented for rapidly computing the lift distributions of arbitrary aerofoils. The numerical results are compared with those obtained by an exact method and for many purposes show a satisfactory degree of accuracy. The latter, for all practically occurring cases, can be estimated at the start of the computation work with the aid of the comparison examples given.

ANALYSIS OF MULTI-RESOURCE LOSS SYSTEM WITH STATE-DEPENDENT ARRIVAL AND SERVICE RATES

2017 ◽  
Vol 31 (4) ◽  
pp. 413-419 ◽  
Author(s):  
Valeriy Naumov ◽  
Konstantin Samouylov
Keyword(s):  
Resource Loss ◽  
Loss System ◽  
Negative Customers ◽  
Loss Model ◽  
State Dependent ◽  
Service Rates ◽  
Erlang Loss

In this paper, we study a generalization of the classical multi-dimensional Erlang loss model with state-dependent arrival and service rates, in which customers at arrival occupy random quantities of various resources and release them at departure. Total amount of resources allocated to customers cannot exceed predefined maximum levels. There can be two types of customers: positive customers, which occupy positive quantities of resources, and negative customers, which occupy negative quantities of resources. Negative customers increase the amount of resources available to positive customers and therefore decrease blocking of positive customers caused by lack of resources.

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