All drawings appearing in this Recommendation have been done in Autocad.
Recommendation E.8501)
CONNECTION RETAINABILITY OBJECTIVE FOR THE
INTERNATIONAL TELEPHONE SERVICE2)
Introduction
This Recommendation is one of a set of Recommendations, comprising
Recommendations E.810, E.830, E.845, E.850 and E.855 concerned with the
accessibility, retainability and integrity of telephone services.
The CCITT,
considering
(a) that "premature release" is defined in Recommendation E.800 as the
event that an established connection will be released for a reason other than
intentionally by any of the parties involved in the call;
(b) that premature release is a measure of connection retainability;
(c) that a prematurely released connection is considered high in annoyance
as perceived by telephone users;
(d) that the probability of a premature release is a function of network
component failure intensity and call holding time;
(e) that the objective should take account of the expectations and
tolerances of users to the premature release impairment as well as the
capabilities of current technology;
(f) that the objective might not be met at the present time but should be
viewed as a long-term goal;
(g) that the objective should take into account the concerns of network
planners and system designers, provide useful guidance to each, and it can be
used by Administrations in a consistent way to measure connection retainability
performance;
(h) that connection retainability is defined in Recommendation E.800,
recommends
1 Definitions
A prematurely released telephone connection is known as a cutoff call when
the connection is completely broken, or
1) when a single interruption occurs lasting for longer than ten seconds
which causes the transmission quality of the connection to be
unsuitable for voice communications;
2) when a succession of interruptions occur lasting less than ten seconds
where the product of the average duration of each interruption and the
frequency of occurrence (i.e., average number of interruptions/seconds)
exceeds 0.005.
performan
performance
The measure to be used shall be the complement of connection
retainability, namely the probability of a prematurely released telephone
connection when normalized to a call holding time of one minute (Pr). The
estimator of the premature release probability is the premature release call
ratio (Pre) which is defined as:
eq Pre = \f(1 V \F(RN,N),T)
where N is the number of telephone calls successfully established in some period
of time, T is the mean call holding time in minutes and RN is the number of
telephone calls successfully completed out of such N calls (see Annex A and Annex
B).
3 Overall objective for premature release probability
The provisional objective for the normalized premature release probability
(Pr) shall be such that the performance is better than the values given below:
for typical international connections:
2 W 10V4 # Pr # 4 W 10V4,
for 90th percentile international connections:
4 W 10V4 # P`r # 8 W 10V4
for worst case international connections:
8 W 10V4 # P"r # 1.6 W 10V3.
Note 1 V It is intended to establish a single value for Pr, P`r or P"r in
the future.
1) Formerly G.181, in Red Book, Fascicle III.1.
2) Some of the terms in this Recommendation, for example, the noun "measure", are used in
the sense of their definition given in Recommendation E.800.
Fascicle II.3 - Rec. E.850 PAGE1
Note 2 V The typical 90th percentile and worst case connections mentioned
above shall be assumed to be those hypothetical reference connections (HRXs)
given in Recommendation E.830.
Note 3 V See Annex B.
4 Allocation of the overall objective
It is desirable, for planning purposes, to allocate the overall objective
for a typical connection to the national systems and the international chain of
the HRX. The overall objective is given by:
Pr = Prn1 + Prn2 + Pri
where Prn1 and Prn2 are the premature release probabilities for originating and
terminating national systems respectively and Pri is the premature release
probability of the international chain. The allocation of the overall objective
to national systems and international chain shall be as follows:
Prn1 = Prn2 = a Pri.
Note 1 V a is provisionally recommended as being equal to 2. Thus, for
example, if:
Pr = 3 x 10-4
then
Prn1 = Prn2 = 1.2 x 10-4
PAGE6 Fascicle II.3 - Rec. E.850
and
Pri = 0.6 x 10-4.
Note 2 - Further allocation of the overall objective to the circuits and
exchanges used in a connection might also be desirable.
Note 3 - Objectives for the permissible probability of premature release
of an established telephone connection in Integrated Digital Networks (IDNs) and
mixed (analogue/digital) networks, due to transit digital or local and combined
local/transit exchange malfunctions, are specified in the Recommendations Q.504
or Q.514.
ANNEX A
(to Recommendation E.850)
Relationship between the premature release probability and its
estimator
The following relationship exists between the premature release
probability normalized to a 1-minute holding time (Pr) and its estimator Pre:
eq \o\ac(lim,\s\do10(N->¥)) Pre = \o\ac(lim,\s\do10(N->¥))\b\bc\(
(\f(1 - \f(RN, N),T)) = Pr, if such limit exists.
On the other hand, for the purpose of network design, the probability of a
premature release with a mean call holding time of T minutes, P(Z, T), can be
expressed using the formula:
P(Z, T) = eq \f( Z,Z + T-1)
where
eq Z = \i\su(i=1,L, ) Zi
and Zi is the average number of failures per minute of an i component in the
hypothetical connection between two users as shown in Figure A-1/E.850. The
connection holding time and the time between failures for the individual
components are assumed to be exponentially distributed.
Figure A-1/E.850 - T0201430-88
Fascicle II.3 - Rec. E.850 PAGE1
In practice, Z « T-1 and therefore Pr can be approximated as follows:
Pr = P(Z, T)T=1 = eq \f( Z,Z + 1) » eq \f(P(Z\, T),T).
Also, the following relationship exists:
eq \o\ac(lim,\s\do10(N->¥))\b\bc\( ( 1 -\f( RN,N)) = P(Z, T).
ANNEX B
(to Recommendation E.850)
A method to estimate the premature release probability
for an international telephone connection
In this annex, a method is described which can be used to estimate the
premature release probability for an international telephone connection.
The method is based on placing end-to-end test calls, whose mean holding
time is T in minutes, and observing those which are prematurely released due
either to transmission or switching failures, or transmission interruptions
lasting longer than ten seconds.
From the results of Annex A, it follows that the simple estimator of Pr
is:
eq Pre = \f(1 - \f( RN,N),T).
If it can be reasonably assumed that the occurrence or non-occurrence of a
premature release for each of the test calls constitutes independent events, then
the binomial sampling theory can be used to derive confidence intervals for Pr,
and to determine minimum sample sizes (N).
In particular, it would be required that N be chosen such that:
Pr { | (RN/N) - PrT | £ e PrT/100 } ³ a/100
where e is the estimation error in percent, and a is the confidence level in
percent. Writing P = Pr x T, it follows from the central limit theorem that, for
large N,
eq \f((eNP), 100) / eq \b\bc\[(NP(1 - P))\s\up4(1/2) ³ Za (B-1)
where Za is the root of the equation:
eq (2/p)1/2 \i(0,Za, ) exp(-1/2y2) dy = a/100.
PAGE6 Fascicle II.3 - Rec. E.850
Neglecting terms of order P2, the inequality (B-1) becomes:
N ³ (100 Za/e)2/P (B-2)
In this last formula, P is generally not known. As an example, however, if
we have to verify that P is in conformity with the overall objectives of typical
connections (see S 3), such that P is in the order of 3 x 10-4, then a choice of
a = 90% and e = 40% would lead to N ³ 56 720.
Similar calculations based on varying assumptions are reproduced in Figure
B-1/E.850.
Based on these results, it is proposed that for an average holding time of
T = 1 min, N = 60 000. For other values of T (in minutes), N = 60 000/T.
Figure B-1/E.850 - CCITT 89360
Bibliography
TORTORELLA (M.): The Bell System Technical Journal, Cutoff calls and telephone
equipment reliability, Vol. 60, No. 8, pp. 1861-1890, October 1981.
Fascicle II.3 - Rec. E.850 PAGE1