Note: Descriptions are shown in the official language in which they were submitted.
202596~
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This invention relates generally to synchronous time
division multiplexing (TDM) of signals and data and, more
particularly, to a TDM system in which a particular signal can be
sampled more than once in a single frame or when synchronous data
is to be transmitted at multiples of some basic rate.
In the conventional TDM communication system a pluralit~
of different slgnals ls sampled perlodlcally in ~equence typlcally
in a voiae communiaation system at a ~ampling rate of 8000
periods/sec. The sampllng perlod or frame ls, therefore, 125 ~sec
long and i8 subdivlded into a plurallty of equal duration time
slots or channels. Each slot is dedicated to a speciflc one of
the sampled slgnals except typically for certain slots which may
be used for signalling and synchronization purposes. Each sample
typically is a pulse aode modulated (~CM) value represented by 8
bits. Such transmlsslon sys~ems exlst ln whlch the number of
slots per frame i9 lO24 and hlgher.
To date, ln all of the conventional ~DM sy~tems, a
particular ~ignal ls sampled only once in each frame. It has been
recognized that a need exi~ts for transmlttlng signals or data of
higher bit rates in the same network serving basic rate data.
However, multi-slot (multi-channel) switching gives rise to
difflculties such as the preservation of time slot order and frame
conslstency.
More particularly, at source encoding, a wide-band
signal will naturally be sampled at equispaced instants in the
frame period (125 ~sec in telephony systems) and at termination
the samples must be delivered to the receiver in the same order
^ 2025969
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and they must belong to the same frame. The network comprises a
number of switching nodes interconnected by trunk groups.
switching node, in turn, may comprise a single-stage time switch
or arrays of time switches interconnected either by links or space
switches. At each time switch, a sample is written during a time
slot 'x' and read out during a designated time slot y'. lsxsN,
l~ysN, N beiny the number of ~lots per frame. The data of lnput-
~lot x an~ output-Ylot y would belon~ to ~he ~ame ~rame lf y ~ x.
Otherwise, the data of slot y would be one frame old. If all the
samples of a call are switched llkèwise, i.e., all in the same
frame or all ln the sub~equent frame, then the connectlon is
frame-consistent and, naturally, the samples can be switched in
the proper order. Attemptlng to satisfy this condition with
independent ~witchlng of the lndivldual channels is sub~ect to
randomness and is llkely to succeed only at very low occupancy
and, even then, sub~ect to certaln restrlctlons. It should be
remembered that ln the swltchlng process the selectlon of eligible
free slots is usually sub~ect to matchlng constraints which differ
in nature accordlng to the internal te~ign of the switch. These
eligiblllty conditions of free tlme slots are not altered by this
lnvention. Call rearrangement (reswltching) of existing
connections to accommodate a new arrival may be used to increase
the traffic capacity (i.e., permissible mean occupancy at a
specified grade of service) of the switching node. However, this
is both impractical and hazardous.
Several solutions have been reported in the literature
(an ex~ensive survey is given in ~1]). Generally, they fall under
:,., . :
--- 2 B ~
71493-47
two categories: post-switching and en route delay equalization.
Post-switching equalization does not result in traffic-capacity
loss but it increases the switching delay since a deep buffer
would be needed at the receiving end. It requires new hardware
and complex software control. En route equalization, in turn, may
be realized in two ways, by frame retention or clever call
paaking.
Wlth p~rticul~r regard to the frame retentlo~ techniquè,
if the tlme switch is designed to store two consecutive frames,
retaining an extra fràme which would not be needed for single
channel calls, then during an output time slot y belonging to
frame f, the data of input time slot x belonging to frames (f, f-
1), if y ~ x, or frames ~f-l, f-2), if y ~ x, would be available
in the data memory. Thu~, the data of time slot x of frame (f-l)
ls always pre~ent durlng frame f, regardless of the relatlve
posltions of x and y in the frame, and frame consistency ls
as~ured with an added round-trip delay of one frame per time
swltch.
~he frame-retention technique doe~ not reduce the
trafflc capacity. However, it doubles the switching delay and its
implementation requires new switching nodes in which the time
switches have deeper data memories (and wider addressing
memories); it is therefore not suitable for multi-stage switching
nodes.
The "call packing" techniques have been well studied for
possible application in telephony switching to reduce matching
loss in certain types of switching nodes. While, under the
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71493-47
restriction of frame consistency, call-packing would offer
significant advantages over first~encounter assignment of multi-
channel calls, it is still wasteful of trunk-group capacity.
Packing is somewhat easier when the number of slots per
frame is a power of two. A slmple packing arrangement of a frame
of N slots would be done wlth the help of a state vector of size N
blts. Blt number 1 ln the state vector stores the ~busy/free)
state of slot J, where ~ i~ the bina~y image of 1~ for example, in
a 1024-slot frame (wlth the slots, numbered 0 to 1023), the index
~0011000001 (decimal lg3) points to the state of frame slot
~ J 10~0001100 ~ declmal 524). The slot numbers need not be stored
ln the state vector. While such a scheme may be reasonably
effective, lt ls still somewhat rigld, lt results ln traffic-
capacity loss, and it lncreases the path asslgnment effort in the
swltch.
The inventlon deals wlth the frame consistency and slot
order problem as follows. Let us flrst conslder a slngle time
~wltah in lsolation and let thè number of slot~ per frame be N,
whiah 1~ typically much larger than the maxlmum number of slots
per call. N ls an even number but need not be a power of two.
The N slots are divlded lnto two segments of N~2 slots each. The
set of m slots of a wide-band call ls divided into two subsets;
one comprises the flrst sl ~ rm/l slots and the other comprlses
the remalnlng s2 = m-sl slots of the call ( r-l denotes rounding
up), the exception belng the slngle-channel calls whlch may be
used to balance the loads of the two segments of the frame. If
the scheme ls followed startlng from source, then the sl slots
2 0 2 5 ~ 6 9 71493-47
will naturally be in the first half of the frame and the s2 slots
will be in the second half. The sl slots of a given call may be
switched to any 51 eligible free slots in the second segment of
the frame while the s2 slots would be switched to any s2 ellgible
free slots in the first segment of the next frame. ~he call
subsets are thus transposed during a slngle stage of tlme
switahing. ~y assigning the selected ~lots in each segment ln an
a~cending order, the outpu~ sample~ o a call will appear in the
proper order but wlll not be properly positioned in the frame.
When the transposed subsets are likewise switched in a second
time-switchlng stage, the call samples will be positioned properly
in the frame. Thus, traversing an even number of time switches,
from source to termination, guarantees both frame conslstency and
the desirable slot order
Within a switching node, or across the internodal
network, the number of time swltching stages may not be even. If
each ~witching node has an even number of time ~tages, then the
technique will always work. I~ the number o~ s~ages i~ odd, then
one of the ~tages should be designed for ~rame retention which has
been discussed earlier. Thus, a single-stage node must employ the
frame retention technlque. This, however would be used
optionally. For example, an intra-node (source-to-source
connection) must use the frame retention capabllity while a
source-to-trunk call would use transposed switching in the node
(thus reducing the switching delay).
The invention may be summarized as in a time-division
multiplexed ~TDM) network having at least one time switching stage
'
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for time switching a TDM transmission, said network organizing
transmitted data into frames, each frame comprising an equal
number of time slots and containing at least one multi-channel
call, a process for efficiently providing high bandwidth
transmissions over said network, the process lncluding the steps
of, dividlng each frame into a first segment and a second segment
each containiny 4ubstantlally the ~ame number of time ~lots,
dividing tha number of ahannèls of the multi-channel call lnto a
first ~ubset and a second subset each containing approximately the
same number of channels, assigning the first subset to the first
segment of the first frame and assigning the second subset to the
second segment of the first frame, and in said tlme switching
stage, transposing the first subset to the second segment of the
first frame such that the channel~ within the first subset occupy
eligible free slots and retain thelr relative order, and
transposing the second subset to the first segment of the next
rame such that the channels within the second subset occupy
eligible free slots and retaln thelr relatlve order.
The invention will now be described in greater detail
with reference to the accompanying drawings in which:
5a
6 ~
71493-47
Figure 1 is a diagram illustrating the problem of slot
order and frame consistency;
Figure 2~ is a diagram illustrating the same problem but
drawn in a cycllc time domain;
Figure 2b is a diagram of the same type as Figure 2a but
illustratlng the lnventlve technlque;
Figure 3a illu~trates schematiaally a network o~ ~lnyle~
stage nodes wlth whlch the lnventlon may be practlsed~
Flgures 3b and 3c lllustrate intra-node and inter-node
swltching, respectlvely, in the network of Figure 3a;
Figure 3d is a graph of blocking versus total occupancy
for the network of Figure 3a comparing the inventlon with other
techniques;
Figure 4a illustrates schematlcally a typlcal tlme-
space-tlme (T-S-T) swltchlng network;
Flgure gb illustrate~ the transposed switchlng technique
as applied to the T-S-T network~
Flgure 4c illu~trates transposèd swltching involving an
odd number o slots per call;
Figure 4d is a graph of blocking versus total occupancy
for the network of Figure 4a;
Figure Sa illustrates schematically a 4-stage node;
Flgure 5b illustrates transposed switching of a five-
slot call in the network of Figure 5a;
Figure 6 illustrates frame retention using a double-
size single buffer in the time switch; and
Figure 7 is a graph of blocking against total occupancy
- 2~2~969
71493-47
for a single concentrator.
With reference to Figure 1, the uppermost row represents
the input of the first time switching stage of a multi-stage
switching sequence. A first sample A is contained in a first slot
of a sixteen slot frame, slot 0 in this example, and a second
~ample B of the same ~i4nal i~ contalned ln a second slot, slot 8
in thls example, the ~lo~ o tha frame belng numbered 0-15.
The second from top row represents the output of the
flxst ~witchlng stage. Sample A ls read out in the fir~t free
~lot of the frame ~ which, for the purposes of thls explanation,
is slot 1. Sample B ls read out in the first free slot appearing
after ~lot 8. It happens that none of the slots 9 to 15 is free
but slot 7 of the subseguent frame F' is and that is where sample
B ls read out. Similarly, durlng the next time switching
operation (between rows 2 and 3) a free slot is found for read out
of sample A ln the same frame, specifically at slot 2 whereas no
free slot for sample B 1~ present between slots 8 and lS. Sample
B has to be read out ln the first available slot of the next frame
F'' which happens to be slot 6 agaln. After four time switching
stages sample B is in frame F'' which is three frames behind
sample A. This pattern is repeated for successlve samples of the
signal for the entire duration of the call.
It should be appreciated that if unpredictable delays
between samples of the same signal occur in this way for every
frame the final output would be meaningless as it could not be
decoded properly, unless we keep track of the delays encountered
in each switching stage and compensate at the receiving end
2~2~
71493-g7
accordingly.
Figure 2a represents exactly the same situation as
Figure 1 except that the information is shown in the cyclic domain
for ease of comparison with Figure 2b.
Turning now to Figure 2b, which illustrates the
teahnique of the lnvention, the frame ls loglcally dlvided into
two equal segment~ of 8 ~lot~ each. ~he flr~t segment or frame
half 1~ denoted Fl and the ~econd ~rame half ~2~
In the example shown, sample A of the slgnal as before
occuples slot 0 and sample B occuples slot 8 as shown ln the top
frame. Thus, sample A ls ln frame half Fl and sample B is in
frame half F2. In the first swltchlng operatlon ~ample A is read
lnto the flrst available ~free) slot of second frame half F2 and
sample B i8 read lnto the flr~t a~allable slot ln the first frame
half Fl' of the next frame F'. Thus, in the posltlon shown at the
second top row sample B 1~ a frame behlnd sample A. In the next
switchlng operatlon, bstween row~ 2 and 3, sample B whl~h 18 ln
the fir~t frame half ~ transposed to the first free slot of
the second frame half F2' and sample A ls transposed from second
frame half F2 to the flrst frame half Fl' of the next frame F'.
Going now from row 3 to 4 sample A is transposed from
frame half Fl' to the second half F2' of the same frame F' and
sample B is transposed from frame half F2' to the first half Fl''
of the next frame F''. Finally, going from row 4 to row 5, sample
A is transposed from frame half F2' to the first half El'' of
Frame F'' and sample B is transposed from the first half Fl'' to
the second half F2'' of the same frame.
- 2 ~ & 9
71493-g7
In the entire switching process samples A and B have
been delayed two frames each and end up in the same frame in the
correct order. Note that the statistical mean delay in traversing
four time switching stages is two frames. Therefore, the
transposition does not indeed lncrease the delay. This example
ean ~lmilarly be extended to any number of slots per slgnal,
provided thi~ number i~ less than tha numbe~ o~ 010ts per frame.
The teehnlque de~eribed above can be used in a network
eomprlsing a number of coneentrating nodes interconnected through
dlstrlbuting nodes. The channel capaclty of a distributing node
is normally much larger than that of a concentrating node. We
analyze the cases of ideal lnternally non-bloeklng nodes and
matehing nodes of the T-S-T strueture. A eoneentrating node may
be eonstrueted as a single time swlteh. The capaeity of a time
swlteh i9 determined prlmarily by the speed limits of its data and
addre~ing memories. At a given switching rate, N slots per
frame, say, a ehannel eapaelty of JN, J > 1, 1Y realized by
parallel eonneetion o~ time ~witehes. A non-bloaking dlstributlng
node may be eonstructed by eonneeting time switehes in a square
matrix. A J x J matrix of N-slot time switehes is equivalent to a
single JN-slot time switch, i.e., it is inherently non-blocking.
The distributing nodes in Figure 3a are assumed to be of this type
and blocking occurs at the inlet/outlet coneentrating stages. The
distribution node of Figure 3a is the subject of U.S. Patent
4,470,139 whieh issued on September 4, 1984. Alternatively, two
arrays of J time switehes may be conneeted by a J x J spaee
2~96~
714g3-47
switch, forming the familiar T-S-T node with a channel capacity of
JN (Figure 4).
With particular regard to Figure 3a, which illustrates a
network of single stage nodes, nodes i, j and k are concentrating
time switching nodes (often called peripheral modules) each of
which may be connected to a source encoder ~not shown) or to a
link from another ~wl~ch. Nodes 1 and ~ are conneated ~o a
distrlbuting node 1 and node ~ is aonnected to a dlstributing node
2. Nodes 1 and 2 are interconnected by a link L. Swltchlng at
the various nodes is controlled by processors (not shown) which
may be programmed to carry out the transposition switching as
described above generally wlth reference to Eigure 2a and as will
be described below speclflcally with reference to Figure 3.
Within a dlstributing node, or across the lnternodal
network, the number of time switches may not be even. If each
dlstributing node has an even number of time stages, then the
tran~posed assignment ylelds frame-conslatent conneations. If the
number of time stages ln a di~trlbutlng node ls odd, then one of
the stages should be designed for frame retention. In the stage
with frame retention the samples of a signal can always be
switched in the proper order at the expense of one-frame delay.
Thus, a single-stage distributing node must employ the frame
retention technique. This, however, would be used optionally.
For example, an intra-node (source-to-source connection) must use
the frame retention capability while a source-to-trunk call would
use transposed switching in the node (thus reducing the switching
delay). This is illustrated in Figure 3b where an 8 slot call
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71493-47
between sources served by the same distributing node uses frame
retention (path I, II, III, IV) and in Figure 3c where a call
traversing two distributing nodes relies only on transposition
(path I, II, V, VI, VII). Erame retention, denoted by symbol ~,
may be implemented in different ways, for example by using a
slngle deep buffer ~double the frame size) as lllustrated in
Figure 6. Such arrangements are well known ln the art and wlll
not be digcu~ed any further.
Figures 4 and 5 lllustrate the cases of a T~S-T network
and a 4-stage network, respectlvely, where frame retentlon is not
needed since the number of tlme stages per node is even. In the T-
S-T structure, an m-slot call is re~ected if the number of free
slots in either of the outer bu~es of the originatlng and
terminating time swltches 15 less than m. Otherwlse, a "temporal"
matchlng process of the free slots of the two inner buses is
performed and the call is accepted if 51 matching slots are found
ln the second half of the frame and s2 ~atchlng slots are found in
the first half. Successfu~ matchlng ls llkely when the number of
free slots in each of the two buses is significantly larger than m
which is a typical case. In the structure of Figure 5, the outer
(origlnating/terminating) stages concentrate the traffic and a
"spatial matching" process in the inner stages is performed when
the number of free slots in each of the originating and
terminating buses in question equals or exceeds m. The matching
is done separately in the upper and lower halves of the frames of
each link and the transposed-assignment scheme is easy to
implement. The spatial matching loss in a well-designed node is
2 ~ 6 9
71493-47
usually negligible compared to the outer blocking.
Figures 4c and 5b illustrate transposed switching when
there is an odd number of slots per call, specifically five in the
examples shown. The slots are divided into three in the first
frame half and two in the second frame half. Alternatively, the
divlslon could be two in the first half and three in the second
half. Elther way of dlvidlng wlll work as long as lt 1~ applied
consistently.
By definitlon, the channel capacity is the a~ailable
number of channels ln the system or component under conslderation
whlle the traflc capacity is the mean occupancy at a specified
grade-of-service (blocking in this case). We determlne the
trafflc capacity of nodes using transposed swltching and compare
wlth the corresponding maxlmum trafflc capacity. We shall flrst
determine the trafflc capacity of an lsolated concentrating tlme-
swltching node wlth unre~trlcted ~lndependent) assignment and
transposed asslgnment ~the unrestrlcted asslgnment can be used
wlth frame retention or po~t-swltchlng equallzatlon). The packlng
method is studied by means of ~imulatlon~
Maximum trafflc capacity is realized with unrestricted
asslgnment. Consider a mixture of traffic streams. The call
intensity of an offered traffic stream is defined as the number of
simultaneous calls in service, while the l oad intenslty is the
number of occupied channels, if the traffic is offered to an
infinite number of channels. For single-channel calls, the call
and load intensities are identical. A traffic stream is
characterized by the parameters ~a, z, m), where "a" is the mean
2 ~ 9
71493-47
load intensity, "z" is the peakedness of the call lntensity, and
"m" is the number of channels required per call. Thus, the mean
load intensity is m-times the mean call intensity, the variance of
the load intensity is m -times the variance of the call intensity,
and the peakedness of the load intensity is mz. The notation (a,
z, m¦n) is used to indicate that the stream (a, z, m) iæ offered
to a 105g sy~tem of n channel~. ~wo 3treams (a~ ml) and ~a~,
z~, ml) are ~ald to be 2-moment-equlvalent lf ea~h of the first
two moments of one stream is equal to the correspondlng moment of
the other, l.e., lf al - a~ and aizimi - ajzjmj. Consider k > 1
traffic ~treams, ~ai,zi,mi, 1 ~ l..k}. If each mi, l-l..k, is
even, then clearly the systems
{(al' Zi' ml) ~ 1 ~ l--k~ ¦ N and { ~ ' Zi' ~ k}¦ _ ,
have identlcal occupancy-blocklng characterlstlcs, i.e.,
transpo~itlon yields exactly the same trafflc performance a~ the
unre~trlcted assignment. Now consider the ca~e where the offered
trafflc include6 a ~lngle-ahannel ~tream, and ~et ~1 ~ 1 for
notatlonal convenience. Then, if ~ ~ mod(mi, 2) ~ al (a
condition which would almo~t always be satisfled), and if each
accepted single-channel arrival is assigned to the frame segment
with the larger number of free channels (or randomly in case of
equality), the states of the two segments would be almost in full
correlation, rendering the capacity reduction due to partitioning
unnoticeable. The analysis of the case of an isolated
concentrating node, with Poissonian or peaked input, is
straightforward ~2]-~5~. In the unrestricted-assignment case we
analyze the system, {ai~ Zi~ Vi ~ i - l..k} ¦N, and in the
13
.:
~v . .
2 Q ~ 9
71493-47
transposed-assignment case we analyze the system: {ai~ Zi' Vi ~ i
= l..k~ In, where ai = ai/2~ vi = rmi /~ '
The extension of the above analysis to a network
interconnecting a large number of concentrating nodes through
single-stage distributing nodes (Flgure 3a) is straightforward.
The maln difference is that the load intensity of each stream is
13a
2025~6~
71493-38
reduced by its downstream blocking. The solution is then
determined by a simple iterative process.
The analysis of matching nodes is ~ore involved. We
shall limit the discussion here to the T-S-T node. Let M be the
number of channels per frame in the inner buses ( II and III in
Flgure 4a). M may be selected to be larger than N, the number of
channals in the outer busei3 (I and IV ln Figure 4a), to faallltate
the matchlng process. At hlgh occupancy, the matchlng lo~s ln
T-S-T nodes increases sharply as the number of slots per call
lncreases and a substantial expanslon ~M~N) ls needed to improve
the efficiency of trunk groups ~oinlng such nodes [6~.
Let the random variables X and Y represent the numbers
of free channels at the inner buses of the orlginating and
termlnating time swltches (or vlce versa). Then, under full
sharlng and wlth unrestrlcted slot a~signment, the mlsniatch
probabllity ~temporal matchlng loss) for an m-channel call ls:
Y-t ~ ~ X 2 m, Y2 m, X~Y ~ M~m,
(ri-O ~ X~Y2M~m. u~ X~m ~Y~m).
In the segmented transposed system, with proper
allocation of single-slot calls, the numbers of free slots in the
upper and lower segments of the frame are equalized, and the
mismatch probability in each segment can be approximated by:
14
2~259~9
71493-38
where x ~ [X/2], y - [Y/2], and m ~ m/2 - 1; L.J denotes
trun¢atlon and j~lrounding-up~ slightly hlgher than ~ ln the
range o~ intere~t, and the occupancy condltlon~ ln the two
~egments are ~trongly correlated. Thus, the net matchlng loss is
~llghtly hlgher than ~. Blocklng occurs due to in~ufflclent free
slots at the lnlet andJor outlet buses (I and IV in Figure 4), or
due to in~ufficient matchlng ~lots in the inner buses ~ II and
III). The perfor~ance is determlned uslng a state-dependent
arrival process [6] and the capacity reduction due to transposed
switching ls shown to be inslgnlflcant.
In the spatial-matching network of Flgure 5, comprising
two concentrating stage~ and two dl~trlbutlng stage~, the spatial
matchlng loss i~ typlcally muah lower than the blocklng in the
outer ~tages and the performance 18 c~mparable to that o the
n ldeal~ network of Flgure 3.
We evaluate the transposition technique by comparison
with the case of unrestricted asslgnment, which ylelds maximum
traffic capacity. The packing solution is studied by means of
simulation for networks employing single-time-stage nodes. The
number of slots per frame is chosen to be 1024, and the offered
traffic comprises three streams of equal offered-load lntenslties
and per-call channel requirements of 1, 8, and 32. We use the
blocXing seen by the 32-slot stream as the grade-of-service.
2~2~69
71493-g7
Eigure 7 shows the load-service characterlstics of an
isolated concentrating node for the cases of unrestricted slot
assignment, transposed assignment, and packed assignment. It is
seen that the blocking with transposed assignment ls
indistlngulshable from that wlth unrestricted assignment whlle the
pac~ing technique yleld~ muah higher bloaklng. The offered
strQam~ are assumed to be Pois~onlan and the analytical solutlon
15 determined by a well-known recurs~on reported in [2]131-
Figure 3d ~hows the end-to-end performance of a network
comprising a large number of identical concentrating nodes,
interconnected through a large non-blocking single-stage
distributing node. The distrlbuting node ls assumed to employ
frame-retention wlth the concentratlng nodes using transposltion
only. The concentratlng nodes are offered equal uncorrelated
traflc loads with a uniform community of lnterest. The
analytical solutlon 1~ obtained by an iterative applicatlon of the
recurslon in 121131, wlth the load lntensity of each stream
reduced by its computed bloaklng (hence the lteratlons).
Flgure 4d sho~s the performance of a T-S-T distributing
node with no expansion in the time stages (M = N in Figure 4).
The solid curve represents the analytical solution, with
unrestricted assignment and with the search for matching slots
starting from a randomly-selected slot. The simulation results
shown are based on starting the search from a fixed slot (or a
fixed slot in each segment in the case of transposition); starting
from a fixed slot reduces the mismatch probability to some extent,
but the corresponding analytical solution is somewhat involved.
--` 20~6~
71493-47
The analytical solution, with the random starting slot, should
serve as an upper-bound for the unrestricted assignment case.
It is seen from these examples that the simple
transposition technique does not result in any noticeable loss of
traffic capacity.
REFERE~CES
[1] Robert~, J.W. and ~oang Van A., "Chara~teristics of Service3
Requlring Multl-Slot Connectlons and thelr Impact on ISDN
Design", Proceedlngs of the flfth ITC Seminar, Lake C'omo,
Italy, May 1987, pp. 97-115.
[2l Roberts, J.W., "A Service Sy~tem with Heterogeneous User
Requirements", Performance of Data Communicatlons Systems and
thelr Applications, G. Pujolle ~Ed.), North Holland (1981).
t3] Xaufman, J.S., "Blocklng ln a Shared Resource Environment",
IEEE Tran~. on Com. Vol. 29, No. 10, pp lg74-1481 l1981).
4l Delbrouck, L.E.N. "On the Steady-State Dlstrlbution in a
Service Facility Carrylng Mlxtures of TrafSic with Different
Peakednes~ ~actor~ and Capacity Requlrements", IEEE Tràns. on
Com. Vol. 31, No. 11, pp 1209-1211 (1983).
0 l5] Beshai, M.E., "The Poissonian Spectrum Method for Treating a
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