DOMAIN EXTENSIONS OF THE ERLANG LOSS FUNCTION: THEIR SCALABILITY AND ITS APPLICATIONS TO COOPERATIVE GAMES

This paper is concerned with the computation of asymptotic blocking probabilities for a generalized Erlangian system which results when M independent Poisson streams of traffic with rates access a trunk group of C circuits with traffic from stream k requiring Ak circuits which are simultaneously held and released after a time which is randomly distributed with unit mean and independent of earlier arrivals and holding times. A call from stream k is lost if on arrival less than Ak circuits are available. Although exact expressions for the blocking probabilities are known, their computation is unwieldy for even moderate-sized switches. It is shown that as the size of the switch increases in that both the traffic rates and trunk capacity are scaled together, simple asymptotic expressions for the blocking probabilities are obtained. In particular the expression is different for light, moderate and heavy loads. The approach is via exponential centering and large deviations and provides a unified framework for the analysis.

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Blocking probabilities for large multirate erlang loss systems

Advances in Applied Probability ◽

10.2307/1427803 ◽

1993 ◽

Vol 25 (4) ◽

pp. 997-1009 ◽

Cited By ~ 34

Author(s):

Pawel Gazdzicki ◽

Ioannis Lambadaris ◽

Ravi R. Mazumdar

Keyword(s):

Large Deviations ◽

Unified Framework ◽

Blocking Probabilities ◽

Asymptotic Expressions ◽

Loss Systems ◽

Heavy Loads ◽

Erlang Loss

This paper is concerned with the computation of asymptotic blocking probabilities for a generalized Erlangian system which results when M independent Poisson streams of traffic with rates access a trunk group of C circuits with traffic from stream k requiring Ak circuits which are simultaneously held and released after a time which is randomly distributed with unit mean and independent of earlier arrivals and holding times. A call from stream k is lost if on arrival less than Ak circuits are available. Although exact expressions for the blocking probabilities are known, their computation is unwieldy for even moderate-sized switches. It is shown that as the size of the switch increases in that both the traffic rates and trunk capacity are scaled together, simple asymptotic expressions for the blocking probabilities are obtained. In particular the expression is different for light, moderate and heavy loads. The approach is via exponential centering and large deviations and provides a unified framework for the analysis.

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Convexity of Functions Which are Generalizations of the Erlang Loss Function and the Erlang Delay Function

SIAM Review ◽

10.1137/1032051 ◽

1990 ◽

Vol 32 (2) ◽

pp. 301-302

Author(s):

A. A. Jagers ◽

E. A. van Doorn

Keyword(s):

Loss Function ◽

Delay Function ◽

Erlang Loss

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A monotonicity result for a single-server loss system

Journal of Applied Probability ◽

10.1017/s0021900200103584 ◽

1995 ◽

Vol 32 (04) ◽

pp. 1112-1117

Author(s):

Xiuli Chao ◽

Liyi Dai

Keyword(s):

Markov Process ◽

Infinitesimal Generator ◽

Blocking Probability ◽

Matrix Analysis ◽

Service Process ◽

Single Server ◽

Loss System ◽

Special Cases ◽

Monotonicity Result ◽

Loss Systems

We consider a family of M(t)/M(t)/1/1 loss systems with arrival and service intensities (λt (c), μt (c)) = (λct , μct ), where (λt , μt ) are governed by an irreducible Markov process with infinitesimal generator Q = (qij )m × m such that (λt , μt ) = (λi , μi ) when the Markov process is in state i. Based on matrix analysis we show that the blocking probability is decreasing in c in the interval [0, c ∗], where c ∗ = 1/maxi Σ j ≠i qij /(λi + μi ). Two special cases are studied for which the result can be extended to all c. These results support Ross's conjecture that a more regular arrival (and service) process leads to a smaller blocking probability.

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On the continued Erlang loss function

Operations Research Letters ◽

10.1016/0167-6377(86)90099-4 ◽

1986 ◽

Vol 5 (1) ◽

pp. 43-46 ◽

Cited By ~ 60

Author(s):

A.A Jagers ◽

Erik A Van Doorn

Keyword(s):

Loss Function ◽

Erlang Loss

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Estimating Effective Capacity in Erlang Loss Systems under Competition

Queueing Systems ◽

10.1007/s11134-004-5554-8 ◽

2005 ◽

Vol 49 (1) ◽

pp. 23-47 ◽

Cited By ~ 2

Author(s):

Andrew M. Ross ◽

J. George Shanthikumar

Keyword(s):

Effective Capacity ◽

Loss Systems ◽

Erlang Loss

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Uncoupled Aspiration Adaptation Dynamics Into the Core

German Economic Review ◽

10.1111/geer.12160 ◽

2019 ◽

Vol 20 (2) ◽

pp. 243-256 ◽

Cited By ~ 4

Author(s):

Heinrich H. Nax

Keyword(s):

Finite Time ◽

Cooperative Games ◽

Transferable Utility ◽

The Core ◽

Best Response ◽

Dynamic Blocking ◽

Evolutionary Interpretation ◽

Require Information ◽

Empty Core

Abstract Dynamics for play of transferable-utility cooperative games are proposed that require information regarding own payoff experiences and other players’ past actions, but not regarding other players’ payoffs. The proposed dynamics provide an evolutionary interpretation of the proto-dynamic ‘blocking argument’ (Edgeworth, 1881) based on the behavioral principles of ‘aspiration adaptation’ (Sauermann and Selten, 1962) instead of best response. If the game has a non-empty core, the dynamics are absorbed into the core in finite time with probability one. If the core is empty, the dynamics cycle infinitely through all coalitions.

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