The Problem

You have been given the job of choosing an admission policy for an ATM multiplexer which has been retrofitted to a local exchange. The multiplexer output is an ATM stream at the STM-16 rate (2.48832 Gb/s). It features two distinct sets of inputs. The first set comprises 6400 voice inputs - these are 32 kb/s ADPCM circuits which are individually mapped into ATM VCs using AAL1. The second set comprises a single IP link, operating at the OC-48 rate, on which is multiplexed all the IP traffic from a corporate intranet. The mux uses AAL5 to convert the incoming IP frames to ATM cells prior to multiplexing.

The mux features a FCFS (First Come First Served) buffer service discipline.

During the busy hour, the mean holding time (i.e., duration) of each voice call is 600 s. Holding times are exponentially distributed. The mean proportion of the number of voice circuits which are busy during the busy hour is 50%. All voice calls are accepted by the mux.

You may assume that the lengths of the IP frames from the corporate intranet are exponentially distributed, with a mean length of 1000 bytes, and that the interarrival time between frames is also exponentially distributed. (You increase the load from the intranet, using this traffic model, by reducing the mean interarrival time). You may (for simplicity) assume that the transmission of ATM cells or IP frames on the various links in the system incurs no overhead due to packet encapsulation at lower levels of the stack or due to the transmission of any "housekeeping" messages. Thus you can assume that the usable bitrate on the STM-16 output link is the full 2.48832 Gb/s, and not say 2.405376 Gb/s (the usable rate after allowing for SDH overhead).

Determine the maximum utilisation of the corporate intranet link which can be permitted if the mean delay through the mux for voice calls is to be kept below 11.755 ms during the busy hour.

Describe carefully any assumptions you make about the internal operation of the mux.