Nov. 7, 2001

The following goes beyond your specific question, but is provided for a
more complete answer.  Assumptions used get at your problem; estimating
the number of 9-1-1 calls to be expected.  Assumptions regarding number
of calls per thousand population, percent of busy day calls to be
expected in the busy hour, and average call times are an average, and
vary from system to system, and community to community.

GRADE OF SERVICE CALCULATIONS

The following information regarding grade of service calculations is
specific to Minnesota conditions and the Minnesota statute and rules
pertaining to 9-1-1 service.

The best way to determine the number of lines needed in a communications
system is to measure actual usage on existing lines over an extended
period of time and at different hours of the day, adjusting the figures
to account for such variables as the number of calls which will still be
answered on the seven-digit numbered lines, the decrease in the length
of the average call due to 9-1-1 feature-induced faster call handling,
and the increase in duplicate calls due to ease of dialing 9-1-1.  This
in-depth analysis requires special skills, is time consuming, and
expensive.  Reasonable estimates are usually sufficient for the initial
design of 9-1-1 systems.  Estimates can be developed by using assumed or
measured demographic and calling characteristics of the population to be
served to calculate the amount of line loading, then referring to a
distribution table, typically a Poisson Table, to determine the number
of lines which would handle that load at the desired grade of service. 
Poisson tables are based on call blockage on the first attempt.  Other
distribution tables, generally available through telephone traffic
engineers, may be more accurate than Poisson tables since they account
for unusual traffic patterns such as peakedness, fast retries of blocked
calls, or all calls overflowing to another PSAP or another telephone
number.

Generally speaking, however, Poisson tables are sufficiently accurate to
provide a good estimate of the number of lines needed.

The following example contains assumptions based on the operational
experience of 9-1-1 systems and guidelines published in the rules for
9-1-1 service.  Local jurisdictional requirements should also be
considered.

Ø There are 1.5 to 3.0 people per telephone main station, our experience
in Minnesota is 2.8 people per telephone main station.

Ø The length of the average 9-1-1 call is 70 seconds, measured from time
of trunk seizure to the time of call termination.  (Some systems outside
of Minnesota are using up to 90 seconds to provide for differences in
technology, training and operations.  No special call handling
techniques, such as pre-arrival instructions, hostage negotiations or
other extenuating circumstances, have been considered in this
calculation.)

Ø An estimated 10% of the calls on the busy day of the average week will
be placed during the busy hour of the day.

Ø One 9-1-1 call per thousand people per day can be expected in a RURAL
area.

Ø Two 9-1-1 calls per thousand people per day can be expected in an area
with over 25,000 population or within five miles of such a SUBURBAN
area.

Ø Three 9-1-1 calls per thousand people per day can be expected in a
city of the first class (Minneapolis, Saint Paul or Duluth) or within 10
miles of

such a METRO area. 

The degree of call handling capacity, loading, on a network is generally 
measured in CCS (Hundred Call Seconds).  CCS can be determined by using
one 
of the following formulas: 

CCS =  ( Population X 70 X 0.1 X CPT )
        -----------------------------
              ( 100 X 1,000 )

OR:

CCS = ( MS X 2.8 X 70 X 0.1 X CPT )
       ---------------------------
             ( 100 X 1,000 )

Where:   MS = Telephone Main Stations
        2.8 = conversion to number of people
        70  = seconds of hold time
        0.1 = conversion to hours (10% of daily calls)
        CPT = Calls per Thousand People per day

By that formula (and using a Poisson table for trunking):               
  
 
                 1 CPT           2 CPT              3 CPT
9-1-1            RURAL          SUBURBAN            METRO
LINES CCS    MS     POP       MS    POP         MS      POP
1     0.4   2,041    5,714    1,020    2,857      680    1,905 
2     5.4  27,551   77,143   13,776   38,571    9,184   25,714 
3    15.7  80,102  224,286   40,051  112,143   26,701   74,762 
4    29.6 151,020  422,857   75,510  211,429   50,340  140,952 
5    46.1 235,204  658,571  117,602  329,286   78,401  219,524 
6    64.4                   164,286  460,000  109,524  306,667 
7    83.9                                     142,687  399,524 
8   105                                       178,571  500,000 
9   126                                       214,286  600,000 


Jim Beutelspacher, ENP
Minnesota Statewide 9-1-1 Program
V-651.296.7104, F-651.297.5368
jim.beutelspacher@state.mn.us
http://www.911.state.mn.us