Florida Institute of technologies ECE 5221 Personal Communication Systems Prepared by: Dr. Ivica Kostanic Lecture 20: Traffic planning (4) Spring 2011

Florida Institute of technologies Page 2  Blocked calls delayed – Erlang C  Traffic estimation in cellular networks Outline Important note: Slides present summary of the results. Detailed derivations are given in notes.

Florida Institute of technologies Page 3 QoS in lossless systems of M/M/C type  M/M/C systems do not reject service requests  If the resources are not available the request is placed in the queue  Queue is assumed infinite  GOS is inadequate measure of QoS  Some examples odispatch voice olow end packet data services (SMS, MMS, , …)  Relevant QoS parameters in lossless systems oProbability of service delay oAverage delay for all requests oAverage delay for the requests placed in the queue o90% delay percentile oAverage number of requests in the queue oProbability of a delay that exceeds a given threshold

Florida Institute of technologies Page 4 Trunking model for lossless systems - Erlang C  Erlang C assumptions oCall arrival process is Poisson oService time is exponentially distributed oThere are C identical servers (channels) oThe queue is infinite  Common QoS parameter in M/M/C systems are odelay probability oaverage delay onumber of users in the queue State diagram of M/M/C system Probability of delay Erlang C delay formula Offered traffic Server utilization

Florida Institute of technologies Page 5 Erlang C - performance curves  Erlang C formula can be given in a form of ofamily of curves otable (Appendix) Erlang C family of curves

Florida Institute of technologies Page 6 Erlang C - Summary of performance parameters Alternative notation Probability of delay exceeding T 1 H – average call holding time

Florida Institute of technologies Page 7 Erlang C - examples Example. Consider a cell site supporting MMS service. Assume that the messages are exponentially distributed with average length of 2 Meg. The cell site provides two channels that have transfer rate of 200kbps. If there are 125 requests per hour estimate probability of 1)Request being delayed 2)Request being delayed by more than 10 sec Answers: Call holding time: 10 sec Average service rate: 0.1 request/sec Birth rate: requests/sec Offered traffic: E Average resource utilization: )Probability of delay: ~ 5% 2)Probability of delay exceeding 10 sec: ~ 1%

Florida Institute of technologies Page 8 Estimation of offered traffic  We need to estimate oGeographical distribution of users oTraffic volume generated per user  Geographical distribution may be estimated using oPopulation density oAverage family income oLand use (clutter) oRoad usage, etc.  Traffic volume may be estimated using oEstimate of call holding time (CHT) oEstimate of number of calls within the busy hour  Once the system is operational traffic data is available from switch reports  Future offered traffic is estimated through the traffic trending process

Florida Institute of technologies Page 9 Estimation of user distribution - example  Estimate user distribution using following GIS and market data oAverage population density oLand use with four morphological classifications (Dense Urban, Urban, Suburban and Rural) oRoad use map with four types of roads (Interstates, Highways, Major roads and Secondary roads) oTotal population in the market and penetration rate  Step 1: Convert all GIS data to relative traffic demand grids  Step 2: Eliminate all GIS data outside of market boundary  Step 3: Determine the total number of users within the boundary  Example of relative weights for the road types Interstates : 10 Highways: 5 Major roads: 3 Second. roads : 1  Example of relative weights for the land use types Dense urban : 10 Urban : 5 Suburban: 3 Rural : 1

Florida Institute of technologies Page 10 Estimation of user distribution - example  Step 4: Use the following “grid algebra” equation where Fraction of users within their residence area Fraction of user distributed through “clutter” Population density relative demand grid Land use demand grid Fraction of users on the roads Total population Penetration rate Roaming factor

Florida Institute of technologies Page 11 Estimation of call holding time (CHT)  Part of CTIA semiannual report  Average CHT for local calls: 2.27 min (136.2)  Average CHT for roaming calls: 3.32min (199.2 sec) DateSubs (connections) Cell sitesAverage monthly bill Average CHT of local call (min) Average CHT of roaming call (min) 2006-Dec233,040,781195,613$ Jun243,428,202210,360$ Dec255,395,599213,299$49.79N/A Jun262,720,165220,472$ Dec270,333,881242,130$ Jun276,610,580245,912$ Dec285,646,191247,081$ Jun292,847,098251,618$ Dec302,859,674253,086$

Florida Institute of technologies Page 12 Estimation of number of calls in busy hour  Average plan (Summer 2011, in FL) o45 dollars per month o450 peak time minutes (from 8:00 AM to 8:00 PM)  Average number of phone calls during week day Assuming that 15% of usage within busy hour - user makes 1.2 calls Traffic per subscriber Note: Homework 5 assigned

Florida Institute of technologies Appendix – Erlang C table Page 13