Network Working Group W. Naylor
Request for Comment: 619 H. Opderbeck
NIC 21990 UCLA-NMC
March 7, 1974
Mean Round-Trip Times in the ARPANET
In one of our current measurement projects we are interested in the
average values of important network parameters. For this purpose we
collect data on the network activity over seven consecutive days. This
data collection is only interrupted by down-time or maintenance of
either the net or our collecting facility (the "late" Sigma-7 or, in
future, the 360/91 at CCN).
The insight gained from the analysis of this data has been reported in
Network Measurement Group Note 18 (NIC 20793):
L. Kleinrock and W. Naylor
"On Measured Behavior of the ARPA Network"
This paper will be presented at the NCC '74 in Chicago.
In this RFCwe want to report the mean round-trip times (or delays) that
were observed during these week-long measurements since we think these
figures are of general interest to the ARPA community. Let us first
define the term "round trip time" as it is used by the statistics
gathering program in the IMPs. When a message is sent from a source
HOST to a destination HOST, the following events, among others, can be
distinguished (T(i) is the time of event i):
T(1): The message is passed from the user program to the NCP in the
source HOST
T(2): The proper entry is made in the pending packet table (PPT) for
single packet messages or the pending leader table (PLT) for
multiple packet messages after the first packet is received by
the source IMP
T(3): The first packet of the message is put on the proper output
queue in the source IMP (at this time the input of the second
packet is initiated)
T(4): The message is put on the HOST-output queue in the destination
IMP (at this time the reassembly of the message is complete)
T(5): The RFNM is sent from the destination IMP to the source IMP
T(6): The RFNM arrives at the source IMP
T(7): The RFNM is accepted by the source HOST
The time intervals T(i)-T(i-1) are mainly due to the following delays
and waiting times:
T(2)-T(1): -HOST processing delay
-HOST-IMP transmission delay for the 32-bit leader
-Waiting time for a message number to become free (only
four messages can simultaneously be transmitted between
any pair of source IMP - destination IMP)
-Waiting time for a buffer to become free (there must be
more than three buffers on the "free buffer list")
-HOST-IMP transmission delay for the first packet
-Waiting time for an entry in the PPT or PLT to become
available (there are eight entries in the PPT and twelve
in the PLT table)
T(3)-T(2): -Waiting time for a store-and-forward (S/F) buffer to
become free (the maximum number of S/F-buffers is 20).
-Waiting time for a logical ACK-channel to become free
(there are 8 logical ACK-channels for each physical
channel).
-For multiple packet messages, waiting time until the
ALLOCATE is received (unless an allocation from a previous
multiple-packet message still exists; such an allocation
is returned in the RFNM and eXPires after 125 msec)
T(4)-T(3): -Queuing delay, transmission delay, and propagation delay
in all the IMPs and lines in the path from source IMP to
destination IMP
-Possibly retransmission delay due to transmission errors
or lack of buffer space (for multiple packet messages the
delays for the individual packets overlap)
T(5)-T(4): -Queuing delay in the destination IMP
-IMP-HOST transmission delay for the first packet
-For multiple-packet messages, waiting time for reassembly
buffers to become free to piggy-back an ALLOCATE on the
RFNM (if this waiting time exceeds one second then the
RFNM is sent without the ALLOCATE)
T(6)-T(5): -Queuing delay, transmission delay, and propagation delay
for the RFNM in all the IMPs and lines in the path from
destination IMP to source IMP
T(7)-T(6): -Queuing delay for the RFNM in the source IMP
-IMP-HOST transmission delay for the RFNM
IMP processing delays are not included in this table since they are
usually very small. Also, some of the abovementioned waiting times
reduce to zero in many cases, e.g. the waiting time for a message number
to become available and the waiting time for a buffer to become free.
If the source and destination HOSTs are attached to the same IMP, this
table can be simplified as follows:
T(2)-T(1): as before
T(3)-T(2): for multiple packet messages: waiting time until
reassembly space becomes available (there are up to 66
reassembly buffers)
T(4)-T(3): for multiple packet messages: HOST-IMP transmission delay
for packets 2,3,...
T(5)-T(4): as before
T(6)-T(5): 0
T(7)-T(6): as before
Up to now we have neglected the possibility that a single packet message
is rejected at the destination IMP because of lack of reassembly space.
If this occurs, the single packet message is treated as a request for
buffer space allocation and the time interval T(3)-T(2) increased by the
waiting time until the corresponding "ALLOCATE" is received.
The round trip time (RTT) is now defined as the time interval T(6)-T(2).
Note that the RTT for multiple packet messages does include the waiting
time until the ALLOCATE is received. It does, however, not include the
source HOST processing delay (i.e. delays in the NCP), the HOST-IMP
transmission delay, and the waiting time until a message number becomes
available. Note also, that the RFNM is sent after the first packet of a
multiple packet message has been received by the destination HOST.
Let us now turn to the presentation of the average round trip times as
they were measured during continuous seven-day periods in August and
December '73. In August, an average number of 2935 messages/minute were
entering the ARPANET. The overall mean round trip delay for all these
messages was 93 milliseconds (msec). The corresponding numbers for
December were 2226 messages/minute and 200 msec. An obvious question
that immediately arises is: why did the average round trip delay more
than double while the rate of incoming messages decreased? The answer
to this question can be found in the large round trip delays for the
status reports that are sent from each IMP to the NCC. Each IMP sends,
on the average, 2.29 status reports per minute to the NCC. Since there
were 45 sites connected to the net in December, a total of 103.05 status
reports per minute were sent to the NCC. Thus 4.63 percent of all
messages that entered the net were status reports.
The average round trip delay for all these status reports in December
was 1.66 sec. This number is five to ten times larger than the average
round-trip delay for status reports we observed in August. It is not
yet clear what change in the collection of status reports caused this
increase. One reason appears to be that the number of these reports was
doubled between August and December. Since the large round-trip delays
of these status reports distort the overall picture somewhat, we are
going to present the December data - wherever appropriate - with and
without the effect of these delays. (We should point out here that the
traffic/delay picture is distorted by the accumulated statistics
messages which were collected to produce this data. We have, however,
ignored this effect since these measurement messages represent less than
0.3% of the total traffic.) The overall mean round trip delay without
the status reports in December is 132 msec. This value is still more
than 35 msec larger than the corresponding value for August. However,
before we shall attempt to explain this difference we will first present
the measured data.
Table 1 shows the mean round trip delay as a function of the number of
hops over the minimum-hop path. This minimum number of hops was
calculated from the (static) topology of the net as it existed in August
and December of last year. The actual number of hops over which any
given message travels may, of course, be larger due to network
congestion, line failures or IMP failures. In fact, for August we
observed a minimum mean path length of 3.24 while the actual measured
mean path length was 3.30; in December we observed 4.02 and 4.40,
respectively. (See Network Measurement Group Note #18 for an
explanation of the computation of actual mean path length.) As expected
we observe a sharp increase of the mean round trip delay as the minimum
number of hops is increased. Note, however, that the mean round trip
delay is not a strictly increasing function of the minimum number of
hops.
Table 2 gives the mean round trip delay for messages from a given site.
The December data is presented with and without the large delays
incurred by the sending of status reports to the NCC. Table 3 shows the
mean round trip delay for messages to a given site. The largest round
trip delays, in December, were incurred by messages sent to the NCC-TIP
since these messages include all the status reports.
Table 4, finally, gives for each site the mean round trip delays to
those three destination IMP/TIP's to which the most messages were sent
during the seven-day measurement period in December. Let us first say
few Words about the traffic distribution which is dealt with in more
detail in Network Measurement Group Note #18. There are several sites
which like to use their IMP as a kind of local multiplexer (UTAH, MIT,
HARV, CMU, USCT, CCAT, XROX, HAWT, MIT2). For these sites the most
favorite destination site is the source IMP itself. For several other
sites the most favorite destination site is just one hop away (BBN,
AMES, AMST, NCCT, RUTT). Nobody will be surprised that for many sites
ISI (ILL, MTRT, ETAT, SDAT, ARPT, RMLT, LONT) or SRI (UCSB, RADT, NBST)
is the most favorite site. There are several other sites (SDC, LL,
CASE, DOCT, BELV, ABRD, FNWT, LBL, NSAT, TYMT, MOFF, WPAT) which were
rather inactive in terms of generating traffic during the seven-day
measurement period in December. Most of their messages were status
reports sent to the NCC. (Those IMPs, for which the frequency of
messages to the NCC-TIP is less than 2.2 messages per minute, were down
for some time during the measurement period).
Let us now attempt to give a few explanations for the overall increase
in the mean round trip delay between August and December. These
explanations may also help to understand the differences in the mean
round trip delays for any given source IMP-destination IMP pair as
observed in Table 4.
1. Frequency of routing messages. Routing messages are the major
source of queuing delay in a very lightly loaded net. In August, a
routing message was sent every 640 msec. Since a routing message is
1160 bits long, 3.625 percent of the bandwidth of a 50 kbs circuit
was used for the sending of routing messages. For randomly arriving
packets this corresponds to a mean queuing delay of 0.42 msec per
hop. Between August and December the frequency of sending routing
messages was made dependent on line speed and line utilization. As
a result, routing messages are now sent on a 50 kbs circuit with
zero load every 128 msec. This corresponds to a line utilization of
18.125 percent and a mean queuing delay of 2.10 msec. The queuing
delay due to routing messages in a very lightly loaded net in
December was therefore five times as large as it was in August.
2. Traffic matrix. The overall mean round trip delay depends on the
traffic matrix. If most of the messages are sent over distances of
0 or 1 hop the overall round trip delay will be small. The heavy
traffic between AMES and AMST over a high-speed circuit in August
contributed to the small overall mean round trip delay.
3. Network topology. The mean round trip delay depends on the number
of hops between source-IMP and destination-IMP and therefore on the
network topology. Disregarding line or IMP failures, the mean
number of hops for a message in August and December was,
respectively, 3.24 and 4.02.
4. Averaging. The network load, given in number or messages per
minute, represents an average over a seven-day period. Even though
this number may be small, considerable queuing delays could have
been incurred during bursts of traffic.
5. Host delays. The round trip delay includes the transmission delay
of the first packet from the destination-IMP to the destination-
HOST; therefore, the mean round trip delay may be influenced by HOST
delays that are independent of the network load.
Table 1 Mean Round Trip Delay as a
Function of the Number of Hops
#MESSAGES/MINUTE #SITE PAIRS MEAN ROUND TRIP DELAY
HOPS AUG DEC AUG DEC AUG DEC DEC
WITH W/OUT
STAT STAT
RPTS RPTS
O 646.9 378.3 39 45 27 44 41
1 487.6 288.7 86 100 25 65 50
2 191.0 143.1 118 138 70 119 80
3 380.7 226.9 148 168 95 131 112
4 218.5 274.1 176 196 102 167 119
5 276.3 185.6 204 228 109 217 134
6 183.8 136.3 210 258 175 355 167
7 333.6 212.7 218 256 178 301 240
8 156.7 161.1 160 234 222 365 241
9 59.0 160.3 102 208 270 308 218
10 0.6 29.9 40 124 331 939 410
11 1.0 18.9 20 46 344 998 699
12 - 10.2 - 20 - 992 655
13 - 0.01 - 4 - 809 809
Table 2 Mean Round Trip Delays for Messages from a Given Site
#MESSAGES/MINUTE MEAN ROUND TRIP DELAY
SITE AUGUST DECEMBER AUGUST DECEMBER DECEMBER
WITH WITHOUT
STATUS STATUS
REPORTS REPORTS
1 UCLA 50.7 40.3 130 282 165
2 SRI 377.3 147.9 45 189 174
3 UCSB 80.2 70.3 120 221 161
4 UTAH 27.0 46.2 136 247 169
5 BBN 120.4 128.3 110 133 133
6 MIT 120.6 96.9 126 160 150
7 RAND 29.3 34.2 127 323 208
8 SDC 1.7 2.4 521 2068 131
9 HARV 50.3 96.0 105 88 72
10 LL 4.4 6.7 201 602 187
11 STAN 49.7 39.7 173 300 191
12 ILL 26.8 53.4 158 216 165
13 CASE 57.6 2.5 138 1592 335
14 CMU 61.1 59.5 153 220 170
15 AMES 242.4 114.1 43 120 81
16 AMST 304.0 163.0 39 94 67
17 MTRT 89.5 60.0 126 199 142
18 RADT 27.7 29.1 145 273 160
19 NBST 98.4 48.2 118 213 152
20 ETAT 24.1 20.6 119 280 119
21 LLL - 6.8 - 721 169
22 ISI 372.0 304.4 110 147 142
23 USCT 298.1 210.3 60 92 70
24 GWCT 10.5 14.1 144 381 102
25 DOCT 5.5 7.0 236 791 171
26 SDAT 14.7 22.9 164 322 177
27 BELV 1.3 2.4 243 1469 466
28 ARPT 57.9 64.3 84 150 93
29 ABRD 1.3 2.4 183 1402 554
30 BBNT 40.8 10.0 75 372 124
31 CCAT 177.7 86.7 83 147 115
32 XROX 56.8 71.7 79 136 78
33 FNWT 2.3 3.5 347 1466 174
34 LBL 1.2 2.7 384 1653 621
35 UCSD 11.9 19.3 237 413 205
36 HAWT 27.5 5.2 654 569 476
37 RMLT 10.4 13.0 122 387 97
40 NCCT - 59.3 - 110 97
41 NSAT 0.6 3.4 1022 1870 1056
42 LONT - 20.8 - 998 848
43 TYMT - 3.7 - 1352 157
44 MIT2 - 5.6 - 720 100
45 MOFF - 2.4 - 1982 447
46 RUTT - 22.4 - 271 153
47 WPAT - 2.7 - 1399 380
Table 3 Mean Round Trip Delay for Messages to a Given Site
#MESSAGES/MINUTE MEAN ROUND TRIP DELAY
SITE AUGUST DECEMBER AUGUST DECEMBER
1 UCLA 57.1 43.5 134 209
2 SRI 382.3 149.4 45 158
3 UCSB 61.1 59.1 117 138
4 UTAH 28.1 50.4 128 159
5 BBN 160.8 149.2 185 110
6 MIT 150.4 107.1 116 130
7 RAND 22.6 25.0 95 161
8 SDC 1.7 0.8 149 174
9 HARV 59.3 98.3 101 70
10 LL 4.6 5.2 195 202
11 STAN 65.3 40.6 135 162
12 ILL 29.1 69.8 156 149
13 CASE 52.6 4.0 127 262
14 CMU 74.8 68.9 135 165
15 AMES 210.3 117.2 40 75
16 AMST 316.7 135.0 38 86
17 MTRT 77.7 51.7 130 151
18 RADT 23.4 23.9 142 202
19 NBST 92.2 39.5 125 169
20 ETAT 25.4 22.8 110 111
21 LLL - 3.7 - 185
22 ISI 361.9 299.2 107 130
23 USCT 298.1 190.6 60 68
24 GWCT 10.5 7.3 144 122
25 DOCT 5.5 4.2 236 187
26 SDAT 13.3 19.7 149 177
27 BELV 0.9 0.9 196 285
28 ARPT 55.4 58.3 78 95
29 ABRD 1.3 0.7 183 271
30 BBNT 40.8 6.4 75 159
31 CCAT 177.7 76.3 83 119
32 XROX 56.8 75.3 79 69
33 FNWT 2.3 1.4 347 165
34 LBL 1.2 0.9 384 305
35 UCSD 11.9 24.0 237 157
36 HAWT 27.5 5.0 654 458
37 RMLT 10.4 11.0 122 97
40 NCCT - 140.1 - 1263
41 NSAT 0.6 1.6 1022 918
42 LONT - 17.3 - 855
43 TYMT - 1.6 - 160
44 MIT2 - 3.9 - 83
45 MOFF - 0.2 - 219
46 RUTT - 14.7 - 153
47 WPAT - 0.5 - 282
Table 4 Mean Round Trip Delay to the Three Most Favorite Sites
#MESSAGES/MINUTE MEAN ROUND TRIP DELAY
FROM SITE TO SITE AUGUST DECEMBER AUGUST DECEMBER
1 UCLA 1 RAND 10.8 9.4 57 92
26 SDAT 5.6 5.9 157 191
22 ISI 3.1 3.1 99 146
2 SRI 12 RADT 16.6 19.5 142 163
17 MTRT 21.9 18.7 140 161
2 SRI 266.1 17.5 14 69
3 UCSB 2 SRI 8.1 17.8 72 68
22 ISI 18.1 17.0 75 86
14 CMU 16.6 11.8 140 152
4 UTAH 4 UTAH 3.5 13.5 136 27
22 ISI 3.7 4.8 131 165
5 BBN 4.2 4.1 168 204
5 BBN 40 NCCT - 81.4 - 105
5 BBN 12.5 19.7 102 37
9 HARV 0.5 9.2 22 37
6 MIT 6 MIT 40.6 24.0 81 85
23 USCT 9.8 13.9 150 173
9 HARV 1.7 12.0 63 88
7 RAND 1 UCLA 12.5 10.4 54 96
16 AMST 0.8 2.6 99 190
40 NCCT - 2.5 - 1941
8 SDC 40 NCCT - 2.2 - 2217
1 UCLA 0.2 0.2 110 136
8 SDC 0.01 0.01 93 13
9 HARV 9 HARV 7.6 50.5 49 21
2 MIT 1.6 11.9 62 85
5 BBN 1.6 9.5 56 37
10 LL 40 NCCT - 2.2 - 1420
10 LL 1.5 1.8 238 135
24 GWCT 0.04 0.6 146 80
11 STAN 14 CMU 3.0 7.0 215 207
4 UTAH 0.2 5.5 117 117
6 MIT 6.5 5.0 186 225
12 ILL 22 ISI 13.3 20.3 146 142
15 AMES 0.8 14.6 109 135
35 UCSD 6.7 6.5 192 269
13 CASE 40 NCCT - 2.2 - 1744
1 UCLA 0.2 0.2 296 400
2 SRI 7.1 0.01 163 316
14 CMU 14 CMU 13.8 23.4 129 94
3 UCSB 13.8 9.2 153 166
11 STAN 3.2 5.1 193 209
15 AMES 16 AMST 205.0 65.8 15 34
12 ILL 1.2 19.6 115 120
31 CCAT 3.2 4.6 174 230
16 AMST 15 AMES 176.8 74.3 13 28
22 ISI 63.6 33.2 50 69
32 XROX 13.3 17.4 41 60
17 MTRT 22 ISI 26.3 27.5 115 118
2 SRI 23.8 20.3 137 155
5 BBN 3.5 4.2 179 133
18 RADT 2 SRI 17.7 21.7 139 156
1 UCLA 0.4 2.3 265 181
40 NCCT - 2.3 - 1618
19 NBST 2 SRI 14.1 12.1 132 163
22 ISI 29.6 11.8 100 117
5 BBN 21.6 9.6 71 97
20 ETAT 22 ISI 11.9 11.3 106 107
24 GWCT 5.0 5.9 99 107
40 NCCT - 2.2 - 1602
21 LLL 5 BBN - 2.9 - 183
40 NCCT - 2.2 - 1847
4 UTAH - 0.5 - 71
22 ISI 28 ARPT 26.0 38.3 106 104
23 USCT 69.0 32.7 80 92
16 AMST 62.0 28.5 53 87
23 USCT 23 USCT 160.9 119.2 19 23
22 ISI 69.2 34.1 78 91
6 MIT 12.9 19.6 135 150
24 GWCT 20 ETAT 6.6 10.8 93 91
40 NCCT - 2.1 - 1978
10 LL 0.03 0.5 359 115
25 DOCT 40 NCCT - 2.3 - 2091
22 ISI 1.0 1.6 220 118
15 AMES 1.9 1.2 167 198
26 SDAT 22 ISI 2.9 8.7 154 138
1 UCLA 5.9 6.0 169 209
2 SRI 1.0 4.4 182 184
27 BELV 40 NCCT - 2.2 - 1553
1 UCLA 0.1 0.2 405 517
22 ISI - 0.01 - 325
28 ARPT 22 ISI 27.4 41.6 106 101
28 ARPT 19.2 13.7 20 35
2 SRI 3.3 3.3 139 157
29 ABRD 40 NCCT - 2.2 - 1461
1 UCLA 0.2 0.2 439 562
9 HARV - 0.01 - 112
30 BBNT 5 BBN 24.2 5.1 36 64
40 NCCT - 2.1 - 1327
22 ISI 4.2 1.1 170 217
31 CCAT 31 CCAT 81.9 28.2 15 31
22 ISI 31.3 23.3 156 171
5 BBN 7.8 7.3 45 42
32 XROX 32 XROX 20.2 36.4 19 15
16 AMST 10.5 13.3 69 93
14 CMU 2.5 3.0 193 251
33 FNWT 40 NCCT - 2.2 - 2210
9 HARV 0.01 0.3 208 194
7 RAND 0.3 0.3 96 171
34 LBL 40 NCCT - 2.4 - 1814
41 NSAT - 0.2 - 1674
1 UCLA 0.1 0.2 295 478
35 UCSD 12 ILL 6.0 7.5 220 260
16 AMST 1.7 4.9 120 172
40 NCCT - 2.0 - 2183
36 HAWT 36 HAWT 0.04 1.6 17 26
22 ISI 5.1 1.0 600 623
15 AMES 2.5 0.8 551 590
37 RMLT 22 ISI 7.5 9.0 68 67
40 NCCT - 2.2 - 1918
28 ARPT - 1.0 - 63
40 NCCT 5 BBN - 41.2 - 33
40 NCCT - 6.6 - 433
22 ISI - 3.2 - 151
41 NSAT 40 NCCT - 2.2 - 2308
2 SRI 0.01 0.4 1046 1002
3 UCSB 0.01 0.2 1169 1018
42 LONT 22 ISI - 6.1 - 837
2 SRI - 3.7 - 884
4 UTAH - 2.2 - 921
43 TYMT 40 NCCT - 2.6 - 1859
2 SRI - 0.5 - 79
3 UCSB - 0.2 - 74
44 MIT2 44 MIT2 - 2.8 - 18
40 NCCT - 2.3 - 1664
1 UCLA - 0.2 - 589
46 MOFF 40 NCCT - 2.2 - 2091
1 UCLA - 0.2 - 447
46 RUTT 9 HARV - 4.3 - 38
5 BBN - 3.5 - 93
22 ISI - 2.9 - 172
47 WPAT 40 NCCT - 2.2 - 1643
3 UCSB - 0.2 - 301
1 UCLA - 0.2 - 671
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