### Palm Probabilities and Stationary Queues

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## Palm Probabilities and Stationary Queues

The inverse operation is called mixing. Given and , the measure a1 is called the mixture of the with respect to and a2 could be called the Fubini formula for mixture measures. A disintegration exists for a -finite if is Polish Borel. This reduces to a matter of conditional distributions.

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The measure is unique up to equivalence, and is unique up to a measurable renormalization -almost everywhere. More generally one studies disintegration or decomposition into slices of a measure on a space relative to any mapping instead of the projection , cf. For each bounded continuous function , let be the expectation of the random variable and let be the measure on.

Then, using a2 , the disintegration of the Campbell measure on yields the measure on and, if is -finite, the can be normalized -almost everywhere to probability measures on to give. The are the Palm distributions Palm probabilities of. Here is the random measure ,.

## On the stationary LCFS-PR single-server queue: A characterization via stochastic intensity

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Views View View source History. Jump to: navigation , search. An important role is played by the factorial moment measures and their extensions is the mathematical expectation and is called the measure of intensity. References [1] A. Khinchin, "Mathematical methods in the theory of queueing" , Griffin Translated from Russian [2] D.

Cox, V. Kerstan, K. Matthes, J. Belyaev, "Elements of the general theory of point processes" Appendix to Russian translation of: H.

Leadbetter, Stationary and related stochastic processes, Wiley, [5] R. Liptser, A. Shiryaev, "Statistics of random processes" , II. Applications , Springer Translated from Russian [6] M. Jacobson, "Statistical analysis of counting processes" , Lect. More generally, for each bounded continuous function on one has the random variable defined by For each random measure one defines the Palm distributions of. The Palm distribution of a random measure is obtained by disintegrating its Campbell measure on , which is given by for , , where is the indicator function of , the function is the pointwise product of the two function and and stands for expectation.

Given a -finite measure on the product space , a disintegration of consists of a -finite measure on and a kernel from to such that -almost everywhere and such that for all , a1 It follows that for every measurable function , a2 The inverse operation is called mixing. Then, using a2 , the disintegration of the Campbell measure on yields the measure on and, if is -finite, the can be normalized -almost everywhere to probability measures on to give The are the Palm distributions Palm probabilities of.

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Here is the random measure , i. References [a1] A. Lewis ed. Murthy, "The general point process" , Addison-Wesley [a4] D. Snyder, "Random point processes" , Wiley [a5] D. Daley, D. Vere-Jones, "An introduction to the theory of point processes" , Springer [a6] F.

## Palm probabilities and stationary queues

Baccelli, P. Neveu, "Processus ponctuels" J. Liggett ed.

Neveu ed. Flour VI , Lect. Press [a10] J. Grandell, "Doubly stochastic Poisson processes" , Springer [a11] H.