Data Communications Networking Devices - 4th Ed.pdf

A.4 APPLYING THE EQUIPMENT SIZING PROCESS ___________________________________ 829when the Erlang formula was used. If the Poisson formula is used a 0.01 grade ofservice based upon 10 erlangs of traf®c requires between 18 and 19 channels.Rounding to the next highest channel results in the Poisson formula providing thesame value as computed previously with the Erlang formula.In general, the Poisson formula produces a more conservative sizing at lowertraf®c intensities than the Erlang formula. At higher traf®c intensities the resultsare reversed. The selection of the appropriate formula depends upon how onevisualizes the calling pattern of users of the communications network.Economic constraintsIn the previous dimensioning exercises the number of trunks or channels selectedwas based upon a de®ned level of grade of service. Although we want to sizeequipment to have a high ef®ciency and keep network users happy, we must alsoconsider the economics of dimensioning. One method that can be used foreconomic analysis is the assignment of a dollar value to each erlang-hour of traf®c.For a company such as a time-sharing service bureau, the assignment of a dollarvalue to each erlang-hour of traf®c may be a simple matter. Here the average revenueper one hour time-sharing session could be computed and used as the dollar valueassigned to each erlang-hour of traf®c. For other organizations, the average hourlyusage of employees waiting service could be employed.As an example of the economics involved in sizing, let us assume lost calls areheld, resulting in traf®c following a Poisson distribution and that 7 erlangs of traf®ccan be expected during the busy hour. Let us suppose we initially desire to offer a0.001 grade of service. From the extract of the execution of the Poisson distributionprogram presented in Table A.6, between 16 and 17 channels would be required.Rounding to the highest number, 17 channels would be selected to provide thedesired 0.001 grade of service.Multiplexers normally consist of a base unit of a number of channels or ports andan expansion chassis into which dual port adapter cards are normally inserted toexpand the capacity of the multiplexer. Many times one may desire to compare thepotential revenue loss in comparison to expanding the multiplexer beyond a certaincapacity. As an example of this consider the data in Table A.7 which indicates thatwhen the traf®c intensity is 5 erlangs a 14-channel multiplexer would provide anequivalent grade of service. This means that during the busy hour 2 erlang hours oftraf®c would be lost and the network designer could then compare the cost of threeadditional ports on the multiplexer and modems and dial-in lines if access to themultiplexer is over the switched network to the loss of revenue by not being able toservice the busy hour traf®c.A.4 APPLYING THE EQUIPMENT SIZING PROCESSMany methods are available for end-users to obtain data traf®c statistics requiredfor sizing communications equipment. Two of the most commonly used methodsare based upon user surveys and computer accounting information.