A new look at the Moran dam

Abstract

For the original Moran dam with independent and identically distributed inputs a representation of the stationary distribution is given which readily provides a geometric rate of convergence to this distribution. For the integer-valued case the stationary distribution can be expressed in terms of simple boundary crossing probabilities for the underlying random walk.

Loss Rate Asymptotics in aGI/G/1 Queue with Finite Buffer

“…[2,4,6,7,20] (however, to some extent (1.3) has been overlooked so that a variety of alternative and typically more complicated representations are around, e.g., Refs. [8,9,19] ). The simplest loss characteristic is the steady-state probability that a customer gets partially rejected, i.e., (e.g., Bekker and Zwart [7] , van Ommeren and de Kok [16] )…”

“…Some examples are dam models with finite capacity (Asmussen [4] Ch. XIV.3, Bekker and Zwart [7] , Moran [14] , Stadje [19] ), waiting time processes in queues with finite capacity (Bekker and Zwart [7] , Cooper, Schmidt and Serfozo [9] , Jelenkovic [10] ) and finite buffer systems in telecommunication models ( Jelenkovic [10] , Kim and Shroff [11] , Zwart [20] ). We will freely alternate between terms such as "overflow", "partial rejection" and "loss" specific for each of these interpretations when referring to the modification of the netput which occurs when Q K n attempts to go above K .…”

Loss Rates for Lévy Processes with Two Reflecting Barriers

“…Among possible applications, we mention finite capacity dam models, buffer systems and queueing systems, see e.g. [2], [4], [9], [10], [15] and [24] and various telecommunication models, see e.g. [10], [13] and [25].…”

“…A first quantity of interest is of course the stationary distribution π K . There are various more or less independent studies around, see in particular [7], [9], [14], [23], [24]. The simplest representation appears to be that of [14], [23], stating that…”

On the Dynamics of Semimartingales with Two Reflecting Barriers

“…Possible applications are buffer systems, finite capacity dam models, and queueing systems (see, e.g. [4], [7], [9], [11], [16], [18], and [21]) and a variety of telecommunication models (see, e.g. [11], [14], and [22]).…”