Data Communications Networking Devices - 4th Ed.pdf

824 _______________________________ SIZING DATA COMMUNICATIONS NETWORK DEVICESFigure A.4 Multiplexer channel sizing. Based upon a busy hour traf®c intensity of 10erlangs, 19 dial-in lines, modems and multiplexer ports would be required to provide a 0.01grade of servicecompany rotary as each dial-in port becomes busy. Thus, traf®c over¯owing dial-inport m is offered to port m + 1 and the traf®c lost by the mth dial-in port, Lm, is thetotal traf®c offered to the entire group of dial-in ports multiplied by the probabilitythat all dial-in ports are busy, thusLm ˆ E P…m; E†where E = traf®c intensity in erlangs and m = number of ports or channels.For the ®rst dial-in port, when m is one, the proportion of traf®c blocked becomesP 1 ˆEE ‡ 1For the second dial-in port, the proportion of traf®c lost by that port becomesP 2 ˆE 2 =2!1 ‡ E ‡…E 2 =2!†In general, the proportion of traf®c lost by the mth port can be expressed asP m ˆX mEm =m!iˆ1…E i =i!†To reduce the complexity of calculation, let us analyze the data traf®c carried by agroup of four dial-in ports connected to a four-channel multiplexer when a traf®cintensity of 3 erlangs is offered to the group.For the ®rst dial-in port, the proportion of lost traf®c becomesP 1 ˆ 33 ‡ 1 ˆ 0:75