scholarly journals M/M/1 queue in two alternating environments and its heavy traffic approximation

2018 ◽  
Vol 465 (2) ◽  
pp. 973-1001 ◽  
Author(s):  
Antonio Di Crescenzo ◽  
Virginia Giorno ◽  
Balasubramanian Krishna Kumar ◽  
Amelia G. Nobile
Keyword(s):  
Heavy Traffic ◽  
Heavy Traffic Approximation

scholarly journals A generalization of Rapp's formula

1982 ◽  
Vol 23 (3) ◽  
pp. 291-296 ◽  
Author(s):  
C. E. M. Pearce
Keyword(s):  
Empirical Result ◽  
Heavy Traffic ◽  
Higher Order ◽  
Theoretical Substantiation ◽  
Heavy Traffic Approximation

AbstractThe Rapp formula of teletraffic dimensioning is generalized to admit an arbitrary renewal stream of offered traffic. The derivation proceeds from a heavy traffic approximation and provides also an estimate of the order of error involved in the Rapp formula. In principle, the method could be used to seek convenient higher order approximations.Our equations give an incidental theoretical substantiation of an empirical result relating to marginal occupancy found recently by Potter.

A second-order heavy traffic approximation for the queue GI/G/1

1981 ◽  
Vol 13 (1) ◽  
pp. 167-185
Author(s):  
Julian Köllerström
Keyword(s):  
Waiting Time ◽  
Order Term ◽  
Heavy Traffic ◽  
Convolution Equation ◽  
Second Order ◽  
First Order ◽  
Functional Convergence ◽  
Ladder Height ◽  
Stationary Waiting Time ◽  
Heavy Traffic Approximation

A second-order heavy traffic approximation for the stationary waiting-time d.f. G for GI/G/1 queues is derived, the first-order term of which is Kingman's (1961), (1962a), (1965) exponential approximation. On the way to this result there are others of independent interest, such as a convolution equation relating this waiting time d.f. G with the d.f. of a related ladder height, an integral equation for G and some stochastic bounds for G. The main result requires a particular type of functional convergence that may also be of interest.

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