Trunking Theory In general, there are many more users than channels--everyone can’t have a permanent personal channel! Fortunately, only a small fraction of total users need a channel at any given time Solution: keep channels in a pool allocate to user when requested return to pool when needed 8/31/98

Trunking Theory(2) Applicable to any system with more customers than resources Basic question: How many subscribers can I have and still guarantee Pr{blocked}< e? 8/31/98

Definitions Grade of Service (GOS): probability that a call is blocked at the busiest time GOS = 2% for AMPS Erlang: unit of traffic intensity, call-hours/hour one call per hour that lasts 1/2 hour constitutes 0.5 Erlangs of traffic 8/31/98

Definitions(2) Offered traffic per subscriber: H is the average call duration msub is the average call requests per unit time per subscriber Total offered traffic from Nsub subscribers: 8/31/98

GOS Calculations We Need: Probabilistic usage model How blocked calls are handled blocked calls cleared blocked calls delayed 8/31/98

Probabilistic Usage Model Call requests are memoryless Time intervals between call requests are independent Pr{call request arrival in Dt} ~ Dt Very unlikely that two requests will occur at exactly the same time Long calls are exponentially less likely than short calls 8/31/98

Blocked Calls Cleared: Erlang B Formula n=number of trunked channels A=total offered traffic 8/31/98

Example 1 Want to start a 900# business to give directions to freshmen A market survey shows: average call arrival rate m=40 calls/hr average call duration for directions is 1/8 hr 2% of freshmen lost is acceptable How many phone operators do I need? 8/31/98

Example 1 Solution 8/31/98

Example 2 (Rappaport Example 2.6) A certain city has an area of 1300 square miles and is covered by a cellular system using a 7-cell reuse pattern. Each cell has a radius of 4 miles and the city is allocated 40 MHz of spectrum with a full duplex channel bandwidth of 60 kHz. Assume a GOS of 2% for an Erlang B system is specified. If the offered traffic per user is 0.03 Erlangs, compute: 8/31/98

Example 2 (cont) (a) number of cells in the service area (b) number of channels per cell (c) traffic intensity of each cell (d) maximum carried traffic (e) total number of users that can be served for 2% GOS (f) number of mobiles per channel (g) theoretical maximum number of users that could be served at one time by the system 8/31/98

Example 2 Solution 8/31/98