Periodic steady state of loss systems with periodic inputs

Helmut Willie

doi:10.1239/aap/1035227997

Periodic steady state of loss systems with periodic inputs

Advances in Applied Probability ◽

10.1017/s0001867800008132 ◽

1998 ◽

Vol 30 (01) ◽

pp. 152-166 ◽

Cited By ~ 2

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.

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

Journal of Applied Probability ◽

10.2307/3214657 ◽

1990 ◽

Vol 27 (2) ◽

pp. 385-392 ◽

Cited By ~ 2

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.

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

Journal of Applied Probability ◽

10.1017/s0021900200038833 ◽

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.

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CONSISTENT PARALLEL AND PROPORTIONAL SHIFTS IN THE TERM STRUCTURE OF FUTURES PRICES

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024915500065 ◽

2015 ◽

Vol 18 (01) ◽

pp. 1550006

Author(s):

MIA HINNERICH

Keyword(s):

Term Structure ◽

Marked Point ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Marked Point Process ◽

Single Factor ◽

Price Model ◽

Futures Price ◽

Necessary And Sufficient ◽

Multidimensional Wiener Process

We consider an arbitrage-free futures price model of Heath–Jarrow–Morton type which is driven by a multidimensional Wiener process and a marked point process. We find necessary and sufficient conditions for this model to produce a log futures curve that changes only through parallel shifts. The same analysis is carried out for the case when the log futures curve changes only through proportional shifts. We prove that there exist nontrivial parallel and proportional shifting log futures curves and we show how to specify the futures price model in order to obtain them. Additionally the shift functions are characterized. Finally, we consider the case of all other single-factor affine models which are neither parallel nor proportional shifting curves. We find necessary and sufficient conditions for the purely Wiener-driven log futures model to admit such other affine shifting curve and we characterize the shift functions.

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Loss Systems with Slow Retrials in the Halfin–Whitt Regime

Advances in Applied Probability ◽

10.1017/s0001867800006273 ◽

2013 ◽

Vol 45 (01) ◽

pp. 274-294 ◽

Cited By ~ 4

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.

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Loss Systems with Slow Retrials in the Halfin–Whitt Regime

Advances in Applied Probability ◽

10.1239/aap/1363354111 ◽

2013 ◽

Vol 45 (1) ◽

pp. 274-294 ◽

Cited By ~ 4

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.

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Connected-Tube MPP Model for Unsupervised 3D Fiber Detection

Electronic Imaging ◽

10.2352/issn.2470-1173.2020.14.coimg-305 ◽

2020 ◽

Vol 2020 (14) ◽

pp. 305-1-305-6

Author(s):

Tianyu Li ◽

Camilo G. Aguilar ◽

Ronald F. Agyei ◽

Imad A. Hanhan ◽

Michael D. Sangid ◽

...

Keyword(s):

Composite Material ◽

Point Process ◽

Marked Point ◽

Experimental Results ◽

Marked Point Process ◽

Fiber Reinforced Composite ◽

Reinforced Composite ◽

Proposed Model ◽

Cylinder Model ◽

Reinforced Composite Material

In this paper, we extend our previous 2D connected-tube marked point process (MPP) model to a 3D connected-tube MPP model for fiber detection. In the 3D case, a tube is represented by a cylinder model with two spherical areas at its ends. The spherical area is used to define connection priors that encourage connection of tubes that belong to the same fiber. Since each long fiber can be fitted by a series of connected short tubes, the proposed model is capable of detecting curved long tubes. We present experimental results on fiber-reinforced composite material images to show the performance of our method.

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