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.

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.

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.

Periodic steady state of loss systems with periodic inputs

1998 ◽  
Vol 30 (1) ◽  
pp. 152-166 ◽  
Author(s):  
Helmut Willie
Keyword(s):  
Steady State ◽  
Marked Point ◽  
Sufficient Conditions ◽  
Initial Distribution ◽  
Marked Point Process ◽  
Loss System ◽  
State Behaviour ◽  
Loss Systems ◽  
Periodic Steady State ◽  
Periodic Inputs

The input of a multiserver loss system is assumed to be a periodic random marked point process which has, with probability one, infinitely many construction points. It is shown that, independently of the initial distribution, there exists a unique periodic process modeling the periodic steady-state behaviour of the loss system. In addition, practical sufficient conditions for the existence of enough construction points are derived.

Periodic steady state of loss systems with periodic inputs

1998 ◽  
Vol 30 (01) ◽  
pp. 152-166 ◽  
Author(s):  
Helmut Willie
Keyword(s):  
Steady State ◽  
Marked Point ◽  
Sufficient Conditions ◽  
Initial Distribution ◽  
Marked Point Process ◽  
Loss System ◽  
State Behaviour ◽  
Loss Systems ◽  
Periodic Steady State ◽  
Periodic Inputs

The input of a multiserver loss system is assumed to be a periodic random marked point process which has, with probability one, infinitely many construction points. It is shown that, independently of the initial distribution, there exists a unique periodic process modeling the periodic steady-state behaviour of the loss system. In addition, practical sufficient conditions for the existence of enough construction points are derived.

scholarly journals Loss Systems with Slow Retrials in the Halfin–Whitt Regime

2013 ◽  
Vol 45 (01) ◽  
pp. 274-294 ◽  
Author(s):  
F. Avram ◽  
A. J. E. M. Janssen ◽  
J. S. H. Van Leeuwaarden
Keyword(s):  
Steady State ◽  
Critical Load ◽  
Performance Measures ◽  
System Performance ◽  
Economies Of Scale ◽  
Blocking Probability ◽  
Loss System ◽  
Qed Regime ◽  
Loss Systems ◽  
Steady State Performance

The Halfin–Whitt regime, or the quality-and-efficiency-driven (QED) regime, for multiserver systems refers to a situation with many servers, a critical load, and yet favorable system performance. We apply this regime to the classical multiserver loss system with slow retrials. We derive nondegenerate limiting expressions for the main steady-state performance measures, including the retrial rate and the blocking probability. It is shown that the economies of scale associated with the QED regime persist for systems with retrials, although in situations when the load becomes extremely critical the retrials cause deteriorated performance. Most of our results are obtained by a detailed analysis of Cohen's equation that defines the retrial rate in an implicit way. The limiting expressions are established by studying prelimit behavior and exploiting the connection between Cohen's equation and Mills' ratio for the Gaussian and Poisson distributions.

scholarly journals Loss Systems with Slow Retrials in the Halfin–Whitt Regime

2013 ◽  
Vol 45 (1) ◽  
pp. 274-294 ◽  
Author(s):  
F. Avram ◽  
A. J. E. M. Janssen ◽  
J. S. H. Van Leeuwaarden
Keyword(s):  
Steady State ◽  
Critical Load ◽  
Performance Measures ◽  
System Performance ◽  
Economies Of Scale ◽  
Blocking Probability ◽  
Loss System ◽  
Qed Regime ◽  
Loss Systems ◽  
Steady State Performance

The Halfin–Whitt regime, or the quality-and-efficiency-driven (QED) regime, for multiserver systems refers to a situation with many servers, a critical load, and yet favorable system performance. We apply this regime to the classical multiserver loss system with slow retrials. We derive nondegenerate limiting expressions for the main steady-state performance measures, including the retrial rate and the blocking probability. It is shown that the economies of scale associated with the QED regime persist for systems with retrials, although in situations when the load becomes extremely critical the retrials cause deteriorated performance. Most of our results are obtained by a detailed analysis of Cohen's equation that defines the retrial rate in an implicit way. The limiting expressions are established by studying prelimit behavior and exploiting the connection between Cohen's equation and Mills' ratio for the Gaussian and Poisson distributions.

Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

2014 ◽  
Vol 14 (04) ◽  
pp. 1450009 ◽  
Author(s):  
Andrew Yee Tak Leung ◽  
Hong Xiang Yang ◽  
Ping Zhu
Keyword(s):  
Steady State ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Homotopy Continuation ◽  
Response Curves ◽  
System A ◽  
Structural Responses ◽  
Voigt Model ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

Adaptation in the respiratory control system

2003 ◽  
Vol 81 (8) ◽  
pp. 765-773 ◽  
Author(s):  
James Duffin ◽  
Safraaz Mahamed
Keyword(s):  
Experimental Data ◽  
Control System ◽  
Steady State ◽  
Graphical Model ◽  
Respiratory Control ◽  
Ventilatory Responses ◽  
System A ◽  
Hypoxia Adaptation ◽  
Peripheral Chemoreflex

Exposure to hypoxia, whether for short or prolonged periods or for repeated episodes, produces alterations in the ventilatory responses. This review presents evidence that these adaptations are likely to be mediated by adaptations in the respiratory chemoreflexes, particularly the peripheral chemoreflex, and proposes models of respiratory control explaining the observed changes in ventilation. After a brief introduction to the respiratory control system, a graphical model is developed that illustrates the operation of the system in the steady state, which will be used later. Next, the adaptations in ventilatory responses to hypoxia that have been observed are described, and methods of measuring the alterations in the chemoreflexes that might account for them are discussed. Finally, experimental data supporting the view that changes in the activity of the peripheral chemoreflex can account for the ventilatory adaptations to hypoxia are presented and incorporated into models of chemoreflex behaviour during exposures to hypoxia of various durations.Key words: respiration, chemoreflexes, hypoxia, adaptation, models.

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.

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