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This is a modified version of the Internet RFC suitable for machine-translating. Original version is available here: RFC619

UNKNOWN
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 RFC we 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
Naylor & Opderbeck                                              [Page 1]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974

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
Naylor & Opderbeck                                              [Page 2]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974
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.
Naylor & Opderbeck                                              [Page 3]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974

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).
Naylor & Opderbeck                                              [Page 4]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974

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.




Naylor & Opderbeck                                              [Page 5]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974


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.
Naylor & Opderbeck                                              [Page 6]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974
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
Naylor & Opderbeck                                              [Page 7]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974
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



Naylor & Opderbeck                                              [Page 8]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974


44  MIT2         -         5.6         -         720       100
45  MOFF         -         2.4         -        1982       447
46  RUTT         -        22.4         -         271       153
47  WPAT         -         2.7         -        1399       380
Naylor & Opderbeck                                              [Page 9]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974
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



Naylor & Opderbeck                                             [Page 10]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974


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


Naylor & Opderbeck                                             [Page 11]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974


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



Naylor & Opderbeck                                             [Page 12]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974


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



Naylor & Opderbeck                                             [Page 13]


RFC 619           Mean Round-Trip Times in the ARPANET        March 1974


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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Naylor & Opderbeck [Page 14]


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