Articles you may be interested inStatistical mechanics of randomflight chains. V Excluded volume expansion and second virial coefficient for linear chains of varying shapeWe consider an nth-order system of ordinary linear differential equations whose coefficients are random functions of the time. In particular, we discuss the case where each of these coefficients is a random noise. A differential equation for the probability distribution of the solutions of the random D. E. is derived and from this the moments can be calculated. Special attention is given to the case of Gaussian noise but the treatment is applicable to any type of noise. Finally, various conditions for stability are discussed.
The following problem is considered: N queues of unrestricted length are served in cyclic order by a single server. Input to each queue is Poisson, the service time distribution may be arbitrary, and a finite time is required by the server to go from one queue to the next. Supposing that at any queue the server serves all units which he finds when he arrives, what is the probability Pn that in a stationary state he finds exactly n units? The method for solving this problem is based on the notion of a "self-consistent" probability distribution and is actually applicable to a general class of multiqueue situations of which the one considered here is typical.
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