Contents Telektronikk - Telenor

previous drops in the MD and from the
IRIM (incoming traffic).
There are assumed n M/M/1 queuing systems
(Markovian input process, Markovian
service time distribution, one server)
with first in first out (FIFO) queue discipline
per PS channel where n is the number
of PS channels. The n channels serve
the whole MD.
The server time is assumed to be proportional
to the packet length with a service
speed of 64 kbit/s. Two traffic models
are given for the PS traffic, the medium
traffic and the high traffic model. The
medium and high traffic model has 10
and 50 call attempts per hour (CAPH)
per subscriber respectively. Each call has
an average of 18 packets with an average
length of 125 bytes. Since both outgoing
and incoming PS calls are queued successively
in all IRSUs and the IRSUs are
considered as one common queue, all
calls are considered outgoing.
The maximum number of ISDN subscribers
in an MD is 512. The results in
the following sections are based on this
number of subscribers. It is important to
note that the tables reflect the total PS
traffic equivalent to 512 subscribers and
that realistic PS traffic will be much
lower due to fewer ISDN subscribers in
an MD.
3.5.3 Results
In the following text and tables the following
abbreviations occur:
λ: Packet arrival rate per second
for a MD
µ: Service rate in packets per
channel
CH: Number of PS channels
CHT: Call Holding Time
CAPH: Call Attempts Per Hour
DELq: Average delay in milliseconds
(ms) for a delayed
packet
DELall: Average delay in ms for all
packets
Qbyte: Average number of queued
bytes per channel
Load: Load per channel
95%_all: Delay in ms for which 95 %
of all packets are below
95%_del: Delay in ms for which 95 %
of the delayed packets are
below.
From Table 1 can be seen that for
medium PS traffic one or two packet
channels are sufficient. For high PS traffic
three or four channels are sufficient,
but one or two channels is impossible
since the load is 2.0 and 1.0 respectively
(a load higher than 1.0 gives an infinite
queue).
The delays depend on the packet length
given the same load. In Table 2 the bytes
per packet and packets per call are interchanged
so that there are many short
packets instead of few long packets.
Short packets reduce the delays and average
queue lengths. Since an objective is
to minimise the number of long delays to
avoid retransmission, shorter packets
may be used.
3.5.4 PS traffic in the signalling
channel
The PS traffic intensity generated by
ISDN subscribers may be so small that
an allocation of one separate PS channel,
and hence a reduction in CS traffic
capacity, would be an unsatisfactory utilisation
of the system. Thus, the signalling
(S) channel may be used as a combined
channel for PS traffic and S traffic. This
solution utilises the spare capacity of the
S channel for PS traffic.
The same queuing model as in the section
‘Analytical model’ has been used.
The abbreviation Wpacket is used for the
weighted average packet length in bytes
based on the distribution of CS and PS
packets.
The ‘2 CH’ and ‘4 CH’ columns in the
tables correspond to a DTRH and a
DTRF configuration respectively.
CAPH and CHT is based on 0.08 Erlang
per subscriber.
CSpackets/call is 88 packets on an average,
i.e. 88 S packets per CS call. CSbytes/packet
is 33 bytes on an average.
This assumes that all traffic carried in the
MD originates and terminates here,
which is a worst case. Approximately 2/3
signalling is for the originating side. 1/3
is for incoming traffic. Since only few
calls use maximal signalling and the rest
is balanced, the theoretical results should
be slightly conservative.
In Table 3 only S traffic is considered.
The results in Table 3 clearly show that
even with high S traffic the load contribution
due to S traffic will be modest
(worst case load-DTRH = 24.8 %). The
average waiting time for all packets will
not exceed 1.35 ms, and 95 % of the
Table 1 PS Traffic
CAPH/SUB 10 50
Bytes/packet 125 125
Packets/call 18 18
λ 25.6 128.0
µ 64 64
1 CH 2 CH 3 CH 4 CH
λ 25.6 12.8 42.7 32.0
Load 0.40 0.20 0.67 0.50
DELq 26.0 19.5 46.9 31.3
DELall 10.4 3.9 31.3 15.6
Qbyte 33.3 6.3 166.7 62.5
95%_del 78 59 140 94
95 %_all 54 27 121 72
Table 2 PS Traffic
CAPH/SUB 10 50
Bytes/packet 18 18
Packets/call 125 125
µ 444 444
1 CH 2 CH 3 CH 4 CH
λ 177.8 88.9 296.3 222.2
Load 0.40 0.20 0.67 0.50
DELq 3.8 2.8 6.8 4.5
DELall 1.5 0.6 4.5 2.2
Qbyte 4.8 0.9 24.0 9.0
95%_del 11 8 20 14
95%_all 8 4 18 10
Table 3 Signalling Traffic
CAPH/SUB 3.2 9.6
cht 90 30
Bytes/packet 33 33
Packets/call 88 88
λ 40.04 120.16
µ 242.42 242.42
2 CH 4 CH 2 CH 4 CH
Load 0.082 0.041 0.248 0.124
DELq 4.4 4.3 5.4 4.7
DELall 0.37 0.18 1.35 0.50
Qbyte 0.25 0.06 2.69 0.58
95%_del 13 12 16 14
93