Subexponential distributions and integrated tails

1988 ◽  
Vol 25 (1) ◽  
pp. 132-141 ◽  
Author(s):  
Claudia Klüppelberg
Keyword(s):  
Distribution Function ◽  
Random Walks ◽  
Wide Class ◽  
Queueing Theory ◽  
Hazard Rate ◽  
Risk Theory ◽  
Subexponential Distributions ◽  
Tail Distribution

Let F be a distribution function on [0,∞) with finite expectation. In terms of the hazard rate of F several conditions are given which simultaneously imply subexponentiality of F and of its integrated tail distribution F1. These conditions apply to a wide class of longtailed distributions, and they can also be used in connection with certain random walks which occur in risk theory and queueing theory.

Subexponential distributions and integrated tails

1988 ◽  
Vol 25 (01) ◽  
pp. 132-141 ◽  
Author(s):  
Claudia Klüppelberg
Keyword(s):  
Distribution Function ◽  
Random Walks ◽  
Wide Class ◽  
Queueing Theory ◽  
Hazard Rate ◽  
Risk Theory ◽  
Subexponential Distributions ◽  
Tail Distribution

Let F be a distribution function on [0,∞) with finite expectation. In terms of the hazard rate of F several conditions are given which simultaneously imply subexponentiality of F and of its integrated tail distribution F 1. These conditions apply to a wide class of longtailed distributions, and they can also be used in connection with certain random walks which occur in risk theory and queueing theory.

BOUNDING THE STATIONARY DISTRIBUTION OF THE M/G/1 QUEUE SIZE

2006 ◽  
Vol 20 (4) ◽  
pp. 571-574 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Stationary Distribution ◽  
Service Time ◽  
Queue Size ◽  
Simple Derivation ◽  
Tail Distribution ◽  
Number Of Customers ◽  
Residual Service

We start with a simple derivation of an identity connecting the conditional expected residual service time as seen by an arrival and the steady-state tail distribution function of the number of customers in the system, which was previously proven by Mandelbaum and Yechiali. We then show how to use it to obtain bounds on the the stationary distribution of the number of customers in the M/G/1 queue.

Dynamic evolution of the averaged distribution function

1982 ◽  
Vol 43 (6) ◽  
pp. 883-891
Author(s):  
H.I. Abdel-Gawad
Keyword(s):  
Distribution Function ◽  
Dynamic Evolution
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