Engset formula for bufferless OBS/OPS: When is and when isn't lengthening the off-time redundant?

To compute link blocking rates in an optical burst/packet switched network, it has been shown that the Engset formula should be used with a reduced packet arrival rate to account for packet dumping. This reduction is realized by lengthening the off-time during which a source remains idle, which is referred to as the lengthened off-time approximation (LOA). It is known that if the blocking probability is small or the number of sources (input links) is large, the LOA is redundant. We show here that the LOA is also redundant for certain state independent approximations and prove that they are equivalent to the Engset formula if the blocking probability is evaluated as a function of utilization. We consider a new LOA whereby the interval by which the off-time is lengthened depends on the number of busy channels. We demonstrate that this new statedependent LOA (sdLOA) yields higher accuracy irrespective of whether blocking probability is evaluated as a function of either utilization which is a system-dependent measure, or system independent measures such as the intended arrival rate.