Stability of single‐wavelength optical buffers

Abstract

SUMMARYOptical burst switching (OBS) provides a future-proof alternative to the current electronic switching in the backbone, but has buffering implemented with a set of fiber delay lines (FDLs). The resulting buffering system fundamentally differs from a classic one, in that the set of possible waiting times is not a continuum (like in the classic case) but rather a denumerable set, each value corresponding to the length of a delay line. As a result, arriving bursts in general have to wait longer than they would in a classic buffer, since their waiting time has to be in that denumerable set. The additional delay results in overall longer waiting times, when compared to a classic infinite buffer system with a continuous waiting room. While previous work already focused on the performance evaluation of finite optical buffers, the stability problem of the infinite system received only little attention. This contribution is the first to present a complete proof of sufficient stability conditions in the case of a general infinite FDL set, general arrival process and general service times. The key elements of analysis is the exploiting of the regenerative property of the waiting-time process and a characterisation of the limiting forward renewal time process. The given bound on the traffic load guarantees stability for a wide class of GI/G/1 optical buffers, and poses no restriction on the FDL lengths.

Stability analysis of multiserver discrete-time queueing systems with renewal-type server interruptions

“…This gives (38). The proof of the 2nd part of Theorem -appearance of a regeneration point in a finite interval -holds unchanged.…”

“…This well-known property (under finite mean interrenewal times) can be obtained from the weak convergence of the residual renewal time to a proper limit in the aperiodic case and also holds when the renewal interval is periodic, for more detail see [35,33]. By the tightness, one can find a constant D < ∞ such that (38) implies, inf…”

“…The key step of the stability analysis presented below is to establish that β(t) ⇒ ∞ (in probability) which implies α 0 < ∞. Such an approach has been successfully applied before, see amongst others [34,38].…”

Stability Analysis of a General State-Dependent Multiserver Queue

“…This approach turns out to be effective in the stability analysis of many queues, including a general retrial queue [22], a multiserver system with non-identical servers [21], and a system with optical buffers [24,29]. Recent applications of the approach are also presented in [23,25].…”

Heuristic performance model of optical buffers for variable length packets

“…Its counterpart for non-degenerate buffer structures is more complicated, as discussed in [18]. In its turn, condition (3) corresponds to some bound ρ max on the traffic load ρ, by definition given by…”