181 lines
7.7 KiB
Plaintext
181 lines
7.7 KiB
Plaintext
EFFICIENT TRAFFIC LOADING OF TELEPHONE LINE GROUPS
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--------------------------------------------------
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Author: Jock Mackirdy
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Business Advisory Services
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Luton, UK
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CompuServe: 100121,1355
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Phone/fax: (44)-1582-597878
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Created 15 March 1994
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Revised 12 April 1994
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Revised 28 January 1995 (revisions marked "*")
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Revised for upload to TELECOMMUNICATIONS Forum
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23 March 1995 (revisions marked "@")
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All comments on content and suggestions for improvement will be
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gratefully received.
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(*) Disclaimer: Telephone traffic theory is based on probability
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and chance, so no solution will be mathematically exact.
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(@) Equally, in measuring traffic, minute accuracy is not needed.
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1. Purpose (* - new para.)
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-------
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Efficient arrangement of telephone lines in a multi-line
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group (exchange lines, inter-PBX links etc.) maximises the
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number of calls carried by the group and minimises the risk of
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call collisions. Improved customer service is allied to minimum
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operating cost.
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2. Background information
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----------------------
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I have applied the standard probability theory of pure chance
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telephone traffic to the specific case of calls to and from a
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multi-line subscriber's installation (usually a switching system
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of some sort).
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The basic data is from graphs in Atkinson's "Telephony", vol 2,
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published 1950 by Pitmans. The mathematics supporting the
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graphs is, as far as I know, in the public domain. It applies
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to pure chance traffic only and becomes less accurate for very
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long call holding times (e.g. dial-up modem links regularly
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connected for more than a few minutes) and installations which
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are regularly overloaded.
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(*) A subscriber's originating traffic is most easily derived by
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analysing telephone bills. Itemised bills (itemising all calls)
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should be analysed to determine the busiest hour of the busiest
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day in the billing period, with all lines taken together.
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For each line, the calls coomencing during this hour should then
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be grouped into five-minute bands.
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There is no need for greater precision, since we are dealing with
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random events (the start and end of individual calls).
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2. Basic tests for a sound installation
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------------------------------------
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The most efficient arrangement is a single group of lines with
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a single telephone number and automatic sequential hunting for
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a free line, with incoming and outgoing calls starting at opposite
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ends of the group of lines.
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(@) It is also the most cost-effective for per-line call discounts,
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since the vast majority of calls will use the very early choice lines.
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The least efficient arrangement, with the greatest chance of a
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busy line or a call collision, is "one number per line" incoming
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combined with a free choice of outgoing line.
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Case 1 One telephone number per line
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------
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A customer dialling any of the published numbers has a high
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probability of finding that number engaged, by either an
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outgoing or incoming call. This can also happen to some extent
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on an installation with "bypass" numbers superimposed on a
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hunting group.
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Case 2 One number for all calls
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------
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The public exchange (US. "office") directs calls to the first
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free line in a pre-determined order. All lines have to be found
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busy before busy tone is returned.
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Case 3 More than one number, in hunting groups
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------
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This is a half-way stage between Cases 1 and 2. It is markedly
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less efficient in usage of lines than Case 2, because a small
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group of lines exhibits the symptoms of Case 1 in not absorbing
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traffic peaks.
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Case 4 Pick any line for outgoing calls
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------
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The risk of call collisions is highest (i.e. accidentally answering
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an incoming call during the 2-sec. (U.K.) silent period of ringing).
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(*) It is also the least effective way of bulking calls for per-line
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discounts.
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Case 5 Sequential hunt for a free outgoing line
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------
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Combined with Case 2, this is the most efficient way to use
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lines. It is important that the subscriber's switch starts
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looking at the LAST incoming line first (the line with the
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greatest chance of being free), and then works backwards in
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sequence.
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3. Improving call-handling efficiency
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----------------------------------
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Step 1 Arrange your installation to apply Case 5 and Case 2.
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------
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Step 2 Examine the number and distribution of calls on the last
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------ year's telephone bills to assess how many lines are needed.
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There are three possibilities; not enough, the right number
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or too many.
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Not enough lines
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----------------
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A subjective test is that incoming calls regularly meet engaged
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tone and/or the business has difficulty finding a free outgoing
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line, even outside peak traffic periods.
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The first objective test is that with reverse hunting (Case 5)
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applied, the first choice outgoing line is not clocking up the
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bulk of calls (at least 75-80% on a 5-line or smaller group, at
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least 50-60% on a larger group up to 10 lines).
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The second objective test is that with Cases 2 and 5 both
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applied, significant numbers of outgoing calls (more than 5% in
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total) are appearing on late choice outgoing lines.
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Right number of lines
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---------------------
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If the volume of incoming and outgoing calls is roughly equal,
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the lines required to carry the outgoing calls are mirrored with
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the rest to give a symmetrical arrangement, in which the
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"middle" line carries no more than 5% of outgoing calls.
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Too many lines
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--------------
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If you improve a badly-designed installation by implementing
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both cases 2 and 5, as many as 50% of the lines can be ceased.
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(*) The "middle" line should be carrying around 5% to 10% of
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outgoing calls during the very busiest hour. If 50% or more
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of lines are carrying no outgoing calls (apart from the odd few
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during peak demand), then lines can be ceased to achieve the
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symmetrical pattern described above.
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4. Calculator for total lines required
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-----------------------------------
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(* totally revised to use the "busy hour" analysis method *)
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One Erlang is the equivalent of a single call lasting one hour.
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Note: I have allowed approx. 1 min. extra per call for dialling
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and the time spent listening to ringing tone and for no-reply calls.
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Total mins. %age o/g calls Lines required Outgoing traffic
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in busy hour on o/g line 1 out total (Erlangs)
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------------ -------------- --- ----- ---------------
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0 - 5 95% 1 2 0-0.1
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5 - 10 85% 2 3-4 0.2
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10 - 20 80% 2 4-5 0.3
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20 - 25 75% 3 5-6 0.4
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25 - 28 70% 3 6 0.5
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28 - 34 63% 4 7-8 0.6
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34 - 40 59% 4 8 0.7
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40 - 50 56% 4 8 0.8
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50 - 55 53% 4 8-9 0.9
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55 - 60 50% 4 8-9 1.0
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You will see how much more efficient a larger group of lines is
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(4 outgoing lines can handle ten times as many calls as 1 line,
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with much better protection against short-term peaks).
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For larger installations (10 lines and above, or bills for over
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25,000 units per quarter), I suggest you seek specialist help.
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I can provide an initial diagnosis from your telephone bills,
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with suggestions for potential improvements and areas to
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investigate further.
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------------------------------------------------------------
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END OF FILE
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