Data Communications Networking Devices - 4th Ed.pdf

A.2 THE ERLANG TRAFFIC FORMULA ______________________________________________ 825The proportion of lost traf®c on the ®rst port multiplied by the offered traf®cprovides the actual amount of lost traf®c on port 1, thusT 1 ˆ P 1 E ˆEE ˆ E2ˆ 2:25 erlangs1 ‡ E 1 ‡ EThe total traf®c carried on the ®rst multiplexer port is the difference between thetotal traf®c offered to that port and the traf®c that over¯ows or is lost to the ®rstport. Denoting the traf®c carried by the ®rst port as C 1 and the amount offered as A,we obtainC 1 ˆ A T 1 ˆ 3 2:25 ˆ 0:75 erlangsSince we consider the rotary as a device that will pass traf®c lost from port one to theremaining ports, we can compute the traf®c lost by the second port in a similarmanner. Substituting in the formula to determine the proportion of traf®c lost, weobtain for the second portP 2 ˆE 2 =2!1 ‡ E ‡…E 2 =2!† ˆ 0:5294The amount of traf®c lost by the second port, T 2 , becomesT 2 ˆ P 2 E ˆ 0:5294 3 ˆ 1:588 erlangsThe traf®c carried by the second port, C 2 , is the difference between the traf®c lostby the ®rst port and the traf®c lost by the second port, thusC 2 ˆ T 1 T 2 ˆ 2:25 1:588 ˆ 0:662 erlangsIn Table A.4, a summary of individual port traf®c statistics are presented for thefour-port multiplexer based upon a traf®c intensity of 3 erlangs offered to thedevice. From Table A.4, the traf®c carried by all four ports totaled 2.3817 erlangs.Since 3 erlangs were offered to the multiplexer ports, then 0.6183 erlangs were lost.The proportion of traf®c lost to the group of four ports is T 4 /E or 0.6183/3 which is0.2061. These calculations become extremely important from a ®nancial standpointTable A.4Individual port traf®c statisticsProportion of Amount of Traf®c carriedPort lost traf®c lost traf®c1 0.7500 2.25 0.752 0.5294 1.588 0.6623 0.3462 1.038 0.5504 0.2061 0.6183 0.4197