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Figs. 1 and 2, which have only one junction circuit in each
direction between each pair of exchanges. Fig. 1 shows a nonhierarchical network; each exchange acts as a tandem for
overflow traffic between the other two, in addition to switching its own originating and terminating traffic. Some of the
possible connections with two calls in progress are as follows:
(1)
(2)
(3)
(4)
(5)
AB,
AC,
ABC,
AC,
AC,
AC
BC
AC
CAB
BCA
In none of these states is it possible to make another connection from A to C. In state 1, both outgoing junctions from A
are busy on calls originating at A. In state 2, both incoming
junctions to C are busy on calls terminating at C. In state 3,
both outgoing junctions from A and both incoming junctions
to C are busy on calls between these exchanges. Thus, in each
of these states, further calls from A to C are prevented by
congestion.
In none of these states is it possible to make another connection from A to C. In states 2, 5, 8, 13 and 15, there are already
two. connections from A to C. In states 4, 7, 9, 11, 12, 14, 16
and 17, there is only one such connection, but all outgoing
junctions from A are busy or all incoming junctions to C are
busy; thus any further connection from A to C is prevented by
congestion.
In states 1, 3, 6 and 10, there is a free circuit outgoing from
A and one incoming to C, but a further connection from A to
C is prevented by blocking. In states 1, 3 and 6, there is one
connection via the tandem exchange which could be made
over a direct junction. In state 10, there are two such connections. These blocking states can be eliminated by replacing
connections via the tandem exchange by direct connections.
Thus, state 1 is replaced by AC, AB, state 3 is replaced by AC,
BC, state 6 is replaced by AB, AC, BC and state 10 is replaced
by AC, AB, BC. Each of these rearrangements makes it possible to make a further connection from A to C via T.
These simple examples show that rearrangement can prevent blocking. The probability of loss is therefore reduced and
a better grade of service is provided. In similar networks
having a plurality of circuits on each route, such blocking
states can arise in association with each of these circuits; it
follows that they can be eliminated as described above. Thus,
it is possible either to improve the grade of service or to
provide fewer circuits. Therefore, just as rearrangement can
enable a switching network in an exchange to use fewer links,
its application to a multiexchange network should enable
fewer circuits to be used. If these circuits are expensive longdistance circuits, the cost saving should be significant.
J. E. FLOOD
1st November 1982
Department of Electrical & Electronic Engineering
The University of Aston in Birmingham
Gosta Green, Birmingham B4 7ET, England
References
Fig. 2 Simple hierarchical network
In state 4, any further connection from A to C is blocked by
a call from C to B that is using A as a tandem exchange,
although junction CB is free. In state 5, a call from B to A is
using C as a tandem exchange, although junction BA is free.
In a network with conventional automatic alternative routing,
these states would not be reached from a state having fewer
connections, since a direct junction would be selected instead
of the indirect route. However, the blocking states are reached
as a result of connections clearing down. For example, state 4
follows the state AC, CB, CAB when connection CB clears
down. Now, connection CAB can be replaced by CB, leaving
AB free; similarly, BCA can be replaced by BA, leaving BC
free. Thus, rearrangement from state 4 or state 5 eliminates
blocking and enables a further connection to be made from A
to C via B.
Fig. 2 shows a hierarchical network in which exchanges A,
B, C act only as local exchanges and exchange T acts only as a
tandem exchange. Some of the possible connections involving
those circuits whose busy/free states are relevant to establishing connections from A to C are as follows:
(1) AC,
(2) AC,
(3) AC,
(4) AB,
(5) AB,
(6) AB,
(7) AC,
(8) AC,
(9) AC,
(10) AC,
(H) AB,
(12) AB,
(13) AB,
(14) AB,
(15) AB,
(16) AC,
(17)
ATB
ATC
BTC
AC,
AC,
AC,
AB,
BC,
BC,
ATB,
AC,
AC,
AC,
AC,
AC,
BC,
AB, AC,
1
AKIYAMA, M., and KAWAGUCHI, K.: 'An alternate routing system
with inquiry control and its traffic characteristics', Electron. &
Commun. Jpn., 1972, 55A, pp. 17-26
2
SZYBICKI, E., and LAVIGNE, M. E. : 'The introduction of an advanced
3
routing system into local digital networks and its impact on the
network economy, reliability and grade of service'. Proc. Int.
Switching Symposium, Paris, May, 1979, pp. 171-177
BENES, v. E.: 'Mathematical theory of connecting networks and
telephone traffic' (Academic Press, 1965)
0013-5194/82/251072-02S1.50/0
ANALYTICAL AND SIMULATION STUDY
OF SIMPLE REARRANGEABLE
MULTIEXCHANGE NETWORKS
Indexing terms: Telecommunication, Switching and switching
circuits
ATB
ATC
BTC
ATB
ATC
BTC
BTC
BC, ATB
BC, BTC
BC, ATC
ATB, BTC
ATC, BTA
ATB, BTC
BC,
ATB, BTC
Congestion probabilities for calls in simple three-exchange
networks operated with and without rearrangements are
determined analytically and by digital simulation. Load-loss
curves are obtained, from which the gain in traffic capacity
due to rearrangement and degradation due to overload can
be found. It is concluded that routing control with rearrangements possesses a potential traffic-handling advantage over conventional automatic alternative routing.
Rearrangement of existing calls is an effective way for reducing congestion in switching networks within exchanges,
since blocking states can be avoided. Benes1 has shown that
the use of rearrangement enables switching networks to be
completely nonblocking. Extensive work has been done on full
and partial rearrangement techniques applied to switching
ELECTRONICS LETTERS 9th December 1982 Vol. 18 No. 25
1073
networks.1 J In a switching network in an exchange, much of
the benefit of rearrangement is outweighed by the control cost
necessary to realise it, especially in the face of decreasing
switch cost. Flood4 has pointed out the potential benefit of
applying rearrangement in the routing control of multiexchange networks. He set out a plan of rearrangement in which
an overflow call in an automatic alternate-routing network is
reswitched through a direct route whenever such a route becomes free by a call clearing down. Flood made a qualitative
assessment of the potential advantages of this rearrangement
policy. This work is an effort to establish a quantitative background for the same problem.
A simple network with three local exchanges with automatic alternative routing is considered for analysis. Two structures are possible for such a network. One, with a hierarchical
arrangement, uses a dedicated tandem exchange T for passing
overflow calls from the direct routes between terminal exchanges A, B and C (Fig. la). The other, with a nonhierarchi-
cal structure, uses a terminal exchange also for tandem
connection of overflow calls between any two of its adjacent
exchanges (Fig. 2a). Two direct routes are then used in tandem
for a single call. These simple structures make basic building
blocks for larger practical networks and their analysis gives an
insight into the performance characteristics of networks of
practical dimensions and complexity. To make it convenient
for accurate analytical study, the structure is further simplified
by considering a network with only one trunk in each direction between each pair of exchanges.
The problem was studied both analytically and by simulation. The analysis was based on the following assumptions:
(a) originating traffic is Poissonian
{b) call holding times are independent with negative exponential distribution and unit mean
(c) each exchange has full access to the outgoing trunks
{d) blocked calls are cleared from the system immediately
without leaving any effect on the traffic flow
(e) occupancy distributions of the trunk groups are independent
(/) the network is in statistical equilibrium
(a) call switching and reswitching times are negligible.
0 0 5 0-10 0-15 0-20 025 030 035 0-40
mm
offered traffic per trunk,erlang
Fig. 1 Simple hierarchical network
a Configuration
b Loss-load curves
c Proportion of calls rearranged
• • O • ' from state equations
- - x - - from Wilkinson theory
—£— from simulation
X3U
010
015 020 025 030 035 040
offered traffic per trunk , erlang mm
Fig. 2 Simple nonhierarchical network
a Configuration
b Loss-load curves
c Proportion of calls rearranged
without rearrangement (state equations)
—O— without rearrangement (simulation)
with rearrangement (state equations)
—A— with rearrangement (simulation)
— ^ — number of rearrangements per call set up (simulation)
1074
State equations were established for the networks shown in
Figs, la and 2a and were solved. However, since the number
of equations increases rapidly with the number of trunks, an
alternative method was sought for application to larger networks.
If an exchange in a hierarchical network has direct routes to
other exchanges and an overflow route to a tandem exchange,
the arrangement is similar to a form of grading that was studied by Wilkinson and Molina.5 In a paper that was published
in 1931, they assumed that calls which seized trunks in the
common overflow group were transferred to individual trunks
as soon as these became free. This appears to have anticipated
the later introduction of rearrangement, although they applied
the analysis to conventional gradings. This analysis has been
modified to replace Wilkinson's 'lost calls held' assumption by
the 'lost calls cleared' assumption and applied to the network
of Fig. la. It gave good agreement with results obtained from
the state equations and the method is readily applicable to
larger networks. However, this method cannot be applied to
the nonhierarchical network of Fig. 2a.
Experimental results corresponding to the above analytical
solutions were obtained by digital simulation of the networks
based on the model mentioned earlier. A roulette model simulation program was used for the purpose. The results represent
mean values of 20 samples taken at intervals of 1000 events, of
which 500 were call arrivals and 500 were call releases. The
means are associated with confidence intervals calculated at
95% confidence levels. In addition to counting the number of
lost calls, the program also counted the number of calls that
were rearranged. This gives a measure of the extra load placed
on the processor of a stored-program-controlled exchange in
order to use this form of routing control.
Loss values for the hierarchical network of Fig. la, obtained
by solving state equations, from the Wilkinson theory and by
simulation, are presented as load-loss curves in Fig. \b. Corresponding curves for the nonhierarchical network, obtained
from the state equations and by simulation, are shown in Fig.
2b. Close agreement between the curves establishes the validity of the mathematical model assumed for the calculation and
simulation. These methods can now be extended for larger
networks.
For these simple networks, the results show that rearrangement enables about 10% to 15% more traffic to be offered to
the hierarchical network at a fixed grade of service. For the
nonhierarchical network, the gain is about 15% to 20%. The
gain in offered traffic is obtained at the cost of additional
processor loading to realise the rearrangement (Figs. \c and
2c). For the simple hierarchical network, the load is about 01
to 0-2 per call set-up; for the nonhierarchical network, the
number of rearrangements is lower.
ELECTRONICS LETTERS 9th December 1982 Vol. 18 No. 25
These preliminary results gives positive indications that a
gain in offered traffic is possible with rearrangement in routing
control. Further study is needed to determine the gain achievable with larger networks.
This work was carried out at the University of Aston in
Birmingham, and acknowledgment is made to the Association
of Commonwealth Universities for the award of a Fellowship
which made this possible.
in the dark and at room temperature. The application of a
forward bias voltage injects excess electrons and holes into an
undoped (i) layer of the diode from an n-type layer and from a
p-type layer of the diode, respectively, and they are trapped
and/or recombine with each other in the i-layer. If the previous explanations are valid, changes in diode characteristics
similar to the PI changes should be observed in this case. In
this letter, we report that we have indeed observed such
changes, and furthermore we have found some differences
between the changes induced by forward bias (FB) carrier
injection and the PI changes.
Samples were prepared by RF glow discharge decomposition of silane. The deposition conditions are reported elsewhere.2-3 In this letter, we report the experimental results for
two samples (sample A and sample B). Sample A was an n-i-ptype a-Si: H diode and its structure was reported elsewhere.3
Sample B was a p-i-n-type a-Si: H diode and its structure was
the same as that reported elsewhere.2 There was a large difference in the stability of diode characteristics against the long
exposure to light between these two types of sample. After 3 h
illumination of AMI light, sample A exhibited 3 considerable
changes both in photovoltaic (PV) and in dark electrical
properties, whereas in sample B only slight changes in dark
electrical properties were observed and no changes occurred in
PV properties. We applied a forward bias voltage ( 1 1 - 2 0 V)
to diodes. The forward bias current density was 1-2 x 10" *
A/cm2, and this value is comparable to the experimental condition reported by Lim et a/.,4 who observed electroluminescence from a-Si:H diodes at room temperature. Therefore,
considerable trapping and recombination of injected carriers
A. K. M. M. RAHMAN KHAN
1st November 1982
Department of Electrical Engineering
Bangladesh University of Engineering & Technology
Dacca, Bangladesh
References
BENES, v. E.: 'Mathematical theory of connecting networks and
telephone traffic' (Academic Press, 1965)
2 BENES, v. E. : 'Traffic in connecting network when existing calls are
rearranged', Bell Syst. Tech. J., 1972, 49, pp. 1471-1481
3 HWANG, F. K.: 'Blocking probabilities for connecting networks allowing rearrangement'. Proc. 8th International Teletraffic
Congress, Melbourne, 1976
4 FLOOD, j . E.: 'Proposed use of rearrangement in multi-exchange
telecommunication networks', see pp. 1072-1073
5 WILKINSON, R. i.: 'The interconnection of telephone systems—
graded multiples', Bell Syst. Tech. J., 1931,10, pp. 531-564
1
0013-5194/82/251073-03$1.50/0
dark
T=300K
CHANGES IN PHOTOVOLTAIC AND DARK
ELECTRICAL PROPERTIES OF
HYDROGENATED AMORPHOUS SILICON
DIODES INDUCED BY FORWARD BIAS
CARRIER INJECTION
E
•ii -3
< 10
Indexing terms: Semiconductor devices and materials, Photovoltaic effects, Electrical conductivity
,o5
The photovoltaic and dark electrical properties of hydrogenated amorphous silicon diodes were changed by forward bias
carrier injection for several hours. These changes were similar to photoinduced (PI) changes previously reported, and
this result supports previous explanations for PI changes.
The differences between these two types of change are also
discussed.
id7
before
1 3
In previous reports,
photoinduced (PI) changes in hydrogenated amorphous silicon (a-Si: H) were thought to be related to trapping and recombination of photogenerated carriers.
To examine the validity of these explanations, we have performed a series of experiments in which a forward bias voltage
was applied to a-Si: H p-i-n and n-i-p diodes for several hours
0-2
0-4
0 6 0-8
voltage, V
10
1-2
BRTTI
Fig. 1 Changes in dark-current/voltage characteristics of sample A by
7 h forward bias carrier injection
Table 1 SUMMARY OF CHANGES IN PHOTOVOLTAIC PROPERTIES OF SAMPLE A
3 h illumination of AMI light
(Pin = 70 mW/cm 2 )
7 h forward bias carrier injection
2
(Pin = 79 mW/cm )
Kc
V
Before
After
(After)
(Before) ( / o )
0-792
0-745
941
FF
Jsc
mA/cm
2
716
4-27
59-6
1f
Kc
V
0-506
0-448
88-5
3•64
1•87
51 •4
0-805
0-783
97-3
Jsc
mA/cm
n
0-505
0-459
3- 67
2- 81
2
618
5-36
86-7
FF
90-9
76- 6
Kc JK> FF, n and Pln in this Table denote open-circuit voltage, short-circuit current, fill factor, conversion efficiency
and the intensity of incident AMI light to measure these properties, respectively. The term '(After)/(Before)' denotes the
ratio of the value of a photovoltaic parameter after the forward bias carrier injection to that before the injection
ELECTRONICS LETTERS 9th December 1982
Vol. 18 No. 25
1075
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