Help with Traffic Engineering

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Help with Traffic Engineering

• Dr. Roger G. Clery
• Roosevelt University
• January 2006 (CC)

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What A Switch Does

• Routes calls / messages to and from senders /
  receivers.
• Concentrates circuits. More Inputs than outputs.
  Saves .
• Causes blockage and delays.
• May collects statistics and billing information.
  

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What An Automatic Call Distributor Does

• Queues customers in line. Makes em wait!
• Distributes calls more evenly to agents.
• May keep statistics on agents
• May be connected to computer system CTI
  Computer Telephone Integration for Screen pops
  to agents

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What Types of Problems Can be Solved

• PBX Private Branch Exchange number of trunks
  required to the CO of the telephone company
• Cellular telephone circuits/ frequencies required
  at cell site.
• Agents required at a call center.
• Circuits/ trunks required between telephone
  switches.
• Trunks/ circuits required for emergency service
  fire, police, security services

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Which Table to Use?

• Calls Queued Agents required Help desk, Call
  center then Erlang C table.
• Emergency services, final routing for telephone
  company or Cell sites Poisson table
• All other use the Erlang B table.

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Components of the Tables

• Lines trunks circuits agents always in
  whole numbers 1,2,3,4 etc.
• Traffic measured in units called Erlangs. One
  Erlang is 3600 seconds of traffic. One Erlang is
  60 minutes of traffic. 3600 seconds 60
  minutes.
• Can also be measured in CCS. One CCS 100
  seconds. 36 CCS 1 Erlang.
• Grade of service. Probability that a call will be
  blocked. Smaller is better! P.01 1 1 out
  of a 100. P 0.1 10 1 out of 10 blocked.

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B Table
Percent Blocked
N Trunks
Traffic in Erlangs
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Poisson Table
Probability of Blockage
Trunks
Traffic in Erlangs
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C Table

• The C table adds some additional information.
• The average length of a call must be known
  usually in minutes
• The probability of blockage is replaced by
  probability of being queued.
• Number of agents replaces number of trunks.
• Average Delay of all calls can be estimated
• Average Delay of Delayed calls can be estimated.
• Probability that a customer will wait a given
  time can be estimated.

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C Table

• Select the correct group based on Erlangs of
  Traffic.For A 0.1 use 1st group.
• Using the Pd, the probability of delay select the
  correct N, for level of service 50.1000 is to
  high0.0048 is best choice available0.0002 is
  too good.

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C Table

• 3. Multiply D1 by Talk time. If Talk time is 12
  minutes then 0.0025 X 12 .03 minutes.03 x 60
  1.8 seconds
• 4. Multiply D2 by Talk time.
• 0.526 x 12 6.312 minutes

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C Table

• 5. Convert all t times to minutes
• .2 x 12 2.4 minutes
• .4 x 12 4.8 minutes
• .6 x 12 7.2 minutes
• .8 x 12 9.6 minutes
• 1 x 12 12 minutes
• 2 x 12 24 minutes
• 3 x 12 36 minutes
• 6. What is the probability of a delay of 9.6
  minutes? .001

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Using a table

• Some judgment is required. If traffic is 2.2
  Erlangs and there is an entry for 2.018 This is
  close enough.
• If you are required to select the grade of
  service consider the consequence. If this is a
  Pizza take out place and an order is lost no big
  deal If you are in cardiac arrest and you are
  calling 911 then this call is very important.

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Solving a problem

• Sam Samarian is opening up an insurance sales
  office. 6 agents will be selling insurance and
  at peek times the will spend 20 minutes per hour
  on the phone. Each agent will have her/his own
  phone on their desk. Each phone is connected to
  the PBX. How many trunks required? Grade of
  service is to be 7 .07
• Solution Minutes of talk 6 x 20 120Erlangs
  120/60 2 ErlangsWhich table PBX no queue
  PBX NO emergency B table

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Solving a problem

• Find .07 Column
• Find 2 Erlangs or better 2.504
• Using this row read to left find N5
• 5 trunks are required.
• Question? What happens if one more trunks is
  added?
• Answer Service improves! Probability of blockage
  goes down to about 0.01

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Solving Another problem

• Butter and Fat Turkey company has a turkey hot
  line for Thanksgiving day. Up to 40 customers
  call in the busy hour and each call takes about 4
  minutes to complete. If the level of service is
  to be lt 8 then how many turkey helpers are
  required? What is the average delay? What is the
  delay of delayed calls?
• Does anybody needing assistance wait 12 minutes?

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Solving Another problem

• How much traffic is generated? 40 X 4 160
  minutes 160/60 2.66 Erlangs
• Which table calls will wait callers will be
  queued C table

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C Table

• 2.66 Closest group is 2.7
• 8 .08 Closest but smaller is 0.0652
• 6 Turkey helpers required
• D1 0.0197
• Delay of all calls is 0.0197 x 4
• 0.0788 minutes 4.728 seconds
• D2 0.303
• Delay of delayed calls is 0.303 x4
• 1.212 minutes
• Delay of 12 minutes?
• t1 4 minutes
• t2 8 minutes
• t3 12 minutes
• There is no value under 3 because the value is
  too small so NO Chance of waiting 12 minutes

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Solving Yet Another Problem

• Cell site on remote mountain is to be connected
  to the MTSO by a microwave link. How many
  channels are required for the voice traffic if
  the max busy hour traffic is 2.5 Erlangs and
  Grade of service is .001

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Solution

• Which table? Poison because of final routing
• Required .001 9 channels 2.453 10 2.961
• I would recommend 10 channels and better service,
  but 9 could squeeze by.
• (note a B table would say 9 is fine handling
  2.56 Erlangs)

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Try this one

• PBX will handle 21 Erlangs and grade of service
  is P 0.05

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Answer

• B Table
• 20.943 close enough to 21
• 26 trunks

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Try this one

• Call Center 45 calls per hour, 8 minutes per
  call, service level 10

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Answer use C table

• 45 x 8 360 minutes
• 360 minutes / 60 6 Erlangs
• A N Pd D1
  D2 PROBABILITY OF DELAY OF TIME t
  
  .2 .4 .6
  .8 1 2 3 4
  6.0 7 0.6138 0.6138 1.000 .503
  .411 .337 .276 .226 .083 .031 .011
  6.0 8 0.3570 0.1785 0.500 .239
  .160 .108 .072 .048 .007 .001 6.0
  9 0.1960 0.0653 0.333 .108 .059
  .032 .018 .010 6.0 10 0.1013 0.0253
  0.250 .046 .020 .009 .004 .002
  6.0 11 0.0492 0.0098 0.200 .018
  .007 .002 .001
• 10 agents 0.1013 ? 10
• .0253 x 8 .2026 minutes 12.14 seconds
• 0.250 x 8 2 minutes
• .002 .2 chance of 6.4 minute delay

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The END

• Clerys Law 82 of any job is understanding the
  problem!