Elements of Queueing Theory: With Applications |
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Page 359
With Applications Thomas L. Saaty. CHAPTER 15 BASIC RENEWAL THEORY 15-1 . Introduction Renewal theory deals essentially with properties of renewals of items that encounter failures and must , therefore , be replaced . The items may be ...
With Applications Thomas L. Saaty. CHAPTER 15 BASIC RENEWAL THEORY 15-1 . Introduction Renewal theory deals essentially with properties of renewals of items that encounter failures and must , therefore , be replaced . The items may be ...
Page 371
... renewal process by Xi if X ; < A , Yi - A if X ; > A , where A is some constant . The new partial sums do not exceed the cor- responding previous ones ; hence the new N , is not less than the previous N. Thus this ... RENEWAL THEORY 371.
... renewal process by Xi if X ; < A , Yi - A if X ; > A , where A is some constant . The new partial sums do not exceed the cor- responding previous ones ; hence the new N , is not less than the previous N. Thus this ... RENEWAL THEORY 371.
Page 403
... Renewal Theory and Its Ramifications , J. Roy . Statist . Soc . , Ser . B , vol . 20 , no . 2 , pp . 243-302 , 1958 . : On the Cumulants of Renewal Processes , Biometrika , vol . 46 , pts . 1-2 , June , 1959 . Infinitesimal Renewal ...
... Renewal Theory and Its Ramifications , J. Roy . Statist . Soc . , Ser . B , vol . 20 , no . 2 , pp . 243-302 , 1958 . : On the Cumulants of Renewal Processes , Biometrika , vol . 46 , pts . 1-2 , June , 1959 . Infinitesimal Renewal ...
Contents
A Description of Queues | 3 |
Poisson Queues | 81 |
NonPoisson Queues | 151 |
Copyright | |
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a₁ aircraft applied arrival occurs assume average number average waiting birth-death busy period calls Chap coefficient compute congestion constant customers delay denote derivative determined equilibrium Erlang's Erlangian example expected number exponential distribution exponential service expression finite given hence independent infinite integral interval jth phase Laplace transform Laplace-Stieltjes transform machines Markoff chain matrix mean moment-generating function multiplied n₁ n₂ Note number of channels number waiting obtained Operations Research p₁ P₁(t parameter Pn(t Po(t Poisson distribution Poisson input Poisson process priority Prob probability distribution queue length queueing problems queueing theory random variables renewal renewal theory result Rouché's theorem served service channel service distribution service rate service-time distribution single-channel queue solution solving Statist steady stochastic process studied theorem tion traffic values variance waiting line waiting-time distribution zero αι λε λι μ₁ Ро