Abstract— We propose a novel approach for modeling the end-to-end time-delay dynamics of the Internet using system identification, and apply it to control real-time telerobotic operations via Internet with specific Quality of Service (QoS) offerings. To do this, we have employed system identification techniques and the ARX model to obtain the values of relevant parameters and study their dynamics. The results show a periodic behavior of the Internet delay. Experimental measurements show the accuracy and usefulness of our theoretical derivations.

I. INTRODUCTION

ELEOPERATION involves control of a plant from a distance that can vary from tens of centimeters

(micromanipulation) to millions of kilometers (space applications). Teleoperation takes several forms and can be done via any communication medium. Recently, the main focus has been on teleoperation via the Internet. Motivated by the availability, widespread access, and low cost of the Internet, many researchers have focused on the Internet-based teleoperation. Since the Internet introduces random communication delays, several challenges, such as loss of transparency and synchronization in real-time closed-loop telerobotic systems, may arise [1]-[3]. To meet these challenges, a general and efficient modeling and analysis tool for the Internet delay is needed.

Understanding the end-to-end packet delay dynamics of the Internet is of crucial importance since it directly affects the Quality of Service (QoS) in real-time applications, and enables us to design an efficient congestion control mechanism for both real-time and non-real-time applications. The queuing theory has been extensively used as a powerful tool to analyze both circuit-switched and packet-switched networks. However, due to its limitations, the queuing theory is not suitable for the analysis of the delay dynamics of the network.

Several measurement-based studies suggest that the end-to-end packet delay in the Internet is quite dynamic [4]-[6]. In the literature, there have been several such studies on the end-to-end packet delay [4]-[5], [7]-[8] and the end-to-end path characteristics [6],[9]. In [4], the end-to-end packet delay and packet loss in the Internet was studied using small UDP probe packets. In [5], the correlation between the actual packet delay and the packet loss was examined. In [8], loss and delay characteristics of a transmission link were

E. Kamrani is with the Department of Electrical Engineering, Islamic Azad University in Garmsar, Iran (e-mail: ehs_kam@yahoo.com)

H. R. Momeni and A. R. Sharafat are with the Department of Electrical Engineering, Tarbiat Modarres University, Tehran, Iran.

presented using end-to-end multicast measurements. In [6], the delay dynamics of the Internet have been analyzed based on measurements of about 20,000 TCP data transfers. In [9], the routing behavior of the Internet has been analyzed using measurements of about 40,000 end-to-end trace route results. In [10], the Internet delay was measured and analyzed at 3 sample nodes in the Internet at random instances, but no description of the delay dynamics was provided. The above studies are limited to the statistical behavior of the end-to-end packet delays and/or path characteristics, and as such, the end-to-end packet delay dynamics of the Internet, which is the main concern of this paper, has not been investigated.

Measurement-based studies have also been applied to the black-box modeling of the network traffic [11]-[14]. In [11], the authors have proposed a traffic model for wide-area TCP traffic by characterizing several distributions of different parameters, such as the packet inter-arrival time and the number of bytes transferred. In [12], the authors have proposed a fast algorithm to construct a Circulant Modulated Rate Process (CMRP) for traffic modeling. In [13], CMRP and Auto-Regressive Moving Average (ARMA) have been used to model the traffic.

In this paper, we study the dynamics of the Internet time-delay, employ the ARX to model the time delays associated with the communications links, and derive the values of its parameters using a system identification approach. This model can be used, in particular, to design an efficient delay-based teleoperation control mechanism using the optimal control theory. We use the ARX model since it is simple, easy to handle, useful in the domain of control theory, and its coefficients are easily determined with little computations.

The rest of this paper is organized as follows. In Section II, teleoperation via networks with specific QoS offerings is discussed. In Section III, we explain and analyze the Internet time-delay using actual measurements. In Section IV, we employ system identification to propose a model for the end-to-end time-delay dynamics of the Internet. Section V contains the results and conclusions.

II. TELEOPERATION IN A QOS NETWORK

A. QoS Parameters

As proposed in [15], the following four parameters, illustrated in Fig. 1, sufficiently describe the network performance in terms of the QoS model: (a) Time delay, (b) Jitter, (c) Bandwidth, and (d) Package loss.

Modeling Internet Delay Dynamics for Teleoperation

Ehsan Kamrani, Hamid R. Momeni, and Ahmad R. Sharafat, Senior Member, IEEE

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Proceedings of the2005 IEEE Conference on Control ApplicationsToronto, Canada, August 28-31, 2005

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0-7803-9354-6/05/$20.00 ©2005 IEEE 1528

B. Time Delay

The delay is the average time, required by a packet to travel from the sender to the receiver. The data transmitted over the Internet, experience a delay, caused by the queuing delay, the processing delay in the switches, and the propagation delay in the links. In a teleoperation scheme in [16], “independent of delay” (IOD) stability was achieved by degrading transparency when the delay was on the rise. To improve the performance, the delays need to be minimized. The impact of other parameters in Fig. 1 can be reduced using existing methods, which usually involve a tradeoff with the delay. Hence, QoS improvement in general involves minimization of the time delay.

Time Delay(T)

Jitter(J) Bandwidth(W)

Package Loss(P)

TeleoperatorHUMANService

Interface (HSI)

QoS communication Network

Fig. 1. Block diagram of a Bilateral teleoperation system

C. Jitter

A crucial component of the end-to-end delay is the random queuing delay in the network devices. Because of these varying delays within the network, the travel time for a packet can fluctuate from a packet to a packet. This phenomenon is called jitter. It is assumed that the end-to-end time delay is given by JT ±1 ,with jitter J representing

a maximum value of variation, represented in Fig. 2(a). In Figs. 2(b) and 2(c), the master and slave position, respectively with and without jitter for two different master signal frequencies are shown. If the maximum jitter is smaller than half width of the strobe impulse of the D/A converter, it will have no effect on the signal. However, usually it is greater than that. The distortion caused by jitter introduces high frequency noise and possible destabilization in the system [17].

As suggested in [15] the following mechanisms are used in combination for the removal of jitter in voice applications: prefacing each chunk with a sequence number, prefacing each chunk with a timestamp, and delaying playout. By employing reconstruction filters, as in [17], the destabilizing effect of jitter is resolved.

D. Band Width

The bandwidth of a link specifies the rate at which data can be transmitted over that link. The required network bandwidth for a teleoperation system depends on the resolution and the sampling rate of position and force signals, and on the protocol used. Since teleoperation is a bandwidth-sensitive application [1], the needed bandwidth

for transmission of haptic data, including the protocol overhead should be reduced. The protocol overhead in UDP is smaller than that of the TCP, furthermore, because a consistent sample rate with lower fluctuations can be maintained with UDP [25], so we opt for the former.

(a)

(b)

(c)

Fig. 2. Master (dash dotted) and slave position with fixed delay (dashed) and with jitter (solid) according to delay in (a)

E. Packet loss

Packet loss is caused by loading the network in excess of its capacity, and results in a network device to drop packets. This parameter depends on the network load and the queuing mechanism used in the network node. Redundancy in sent packets, such as in the forward error correction (FEC) scheme, compensates for lost packets. UDP is preferred also in this aspect

III. INTERNET DELAY MEASUREMENTS

A. Delay Dynamics of Internet in Iran

We have measured the delay for a number of Internet nodes in different geographical locations in Iran as well as another international node for different time intervals. Statistical results are shown in Table 1. Furthermore, we have measured the delay between two given nodes (denoted by IP1 and IP2) between these two and other nodes identified in Table 1. The results are shown in Tables 2 to 5. Fig. 3 shows the variations in the delay during a 24 hour period with sampling at 1 min intervals. Fig. 4 shows the same, but for a sampling interval of 10 minutes. Figs. 5-6 show the measured delay during one month with sampling intervals of 12 and 24 hours, respectively. Finally, Figs. 7-8 show the measured delay for a 20 weeks and for a one year period with sampling intervals of one week and one month,

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respectively. Measurements in each interval have been done independent from other intervals.

It is evident in Fig. 3 that the 24 hour delay dynamics is periodic, such that the delay in the early hours and the late hours of the day is high, and decreasing in between during the day. For longer sampling intervals, we do not see the significant instantaneous delay variations (called blackouts) that are present in measurements for shorter sampling intervals. This is an illusion, and can lead to instability in the system if the said blackouts are ignored. We also note that despite the chaotic nature of the Internet delays, it is a cyclic phenomenon with a period of 24 hours.

Fig. 9 shows that the Round Trip Time (RTT) for a sample link in one week, taken from the NLANR Active Measurement Project (AMP). It has a similar (i.e., cyclic) nature similar to our own measurements.

Table 1. Characteristics of the measured delay in some Internet nodes

Place Avg. Delay

(ms) Std. Dev.

(ms) Maximum delay(ms)

Minimum delay(ms)

Sistan Univ. 846.01 38.6454 1381 639

Tabriz Univ. 930.75 94.2156 1931 723

T.M.U 1911.55 83.0866 2831 691

yahoo.com 189.26 61.0934 337 86

Table 2. The average delay between master and slave

Delay (ms) Delay (ms) Place

IP1 IP2

Sistan Univ. 781 896

Tabriz Univ. 812 937

T.M.U 950 1112

yahoo.com 102 136.5

Table 3. The Std. deviation of delay between master and slave

Delay (ms) Delay (ms) Std. deviation

IP1 IP2

Sistan Univ. 34 48

Tabriz Univ. 38 62

T.M.U 53 61

yahoo.com 23 41

Table 4. The maximum delay between master and slave

Delay (ms) Delay (ms) maximum

IP1 IP2

Sistan Univ. 832 956

Tabriz Univ. 896 972

T.M.U 1003 1418

yahoo.com139 191

Table 5. The minimum delay between master and slave

Delay (ms) Delay (ms) minimum

IP1 IP2

Sistan Univ. 701 712

Tabriz Univ. 613 663

T.M.U 659 701

yahoo.com 97 102

24Hour_Time Delay(sample rate=1/min)

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Fig. 9. A week long RTT display for an sample link in AMP

The Return Level [18] is a value expected to occur exactly once during the Return period. Fig. 10 shows the statistical result of Return Levels for five different return periods. We observe that larger return periods result in larger values of Return Levels.

Fig. 10. Return Levels for five different return periods

From the measurements we note a cyclic behavior despite the chaotic nature of the Internet delay. We also note sudden and enormous changes in delay dynamics. Some control schemes have been proposed in [19],[20] and [23]-[26] to make the teleoperator system robust against variations in the Internet delays.

IV. MODELING INTERNET DELAY DYNAMICS

A. Black-Box Model of Internet Delay Using ARX

The end-to-end packet delay dynamics is modeled as a Single-Input-Single-Output SISO) system. We use the Auto-Regressive eXogenous (ARX) model and determine its coefficients using system identification approach. Since the ARX is a linear time-invariant model, it cannot rigorously capture the non-linearity of the packet delay dynamics. Nevertheless, the ARX model is applied in many control engineering problems, because non-linearity around a stable operating point can be well approximated by a linear system.

Fig. 11. The ARX model for the end-to- end packet delay dynamics

The input is the inter-departure times between packets leaving the source, and the output is an end-to-end packet delay measured at the destination. Effects of other traffic (i.e., packets coming from other hosts) are modeled as noise in the ARX model. As implied in [27], the aggregated

network traffic is not stationary, so in order to reduce non-stationarity of noise, we choose the end-to-end packet delay variation, instead of end-to-end packet delay itself (Fig. 11). The input to the ARX model is the inter-departure time (u[k]). In unilateral teleoperation applications, this is constant and determined by the control frequency. Therefore, given a constant input, the predicted output (end-to-end packet delay) would also become constant after the transient period. Consequently, the dynamic model may appear to be irrelevant for teleoperation applications, but in bilateral teleoperation (which is the main focus of our modeling applications), the model can be used. Furthermore even in a unilateral teleoperation we can use random inter-departure times in order to address the delay effects on system dynamics.

To determine the coefficients of the ARX model, a few sets of input and output data are obtained from simulations using NS2 [21] and from our own measurements. We consider two cases: (a) each host sends only UDP packets and (b) each host sends both UDP and TCP packets. Shown in Figs. 12 and 13 are the inter-departure time u(k) and the end-to-end packet delay variation y(k) for the UDP and the UDP + TCP cases, respectively.

(a)

(b) Fig. 12. (a) Packet inter-departure time u(k) (b) End-to-end packet delay variation y(k) in UDP case

(a)

(b) Fig. 13. (a) Packet inter-departure time u(k) (b) End-to-end packet delay variation y(k) in UDP+TCP case

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Let u(k) and y(k) be the input and the output data at slot k.The ARX model is

1121

11

...)(

)1(...1)(

)()()()()(

+−−

−−

+++=

+++=

+−=

b

b

a

a

nn

nn

d

qbqbbqB

qaqaqA

kenkuqBkyqA

where e(k) is noise, 1−q is the delay operator; i.e.,

)1()(1 −≡− kukuq , an and bn are the orders of

respective polynomials, dn is the delay from the input to the

output [22], and ],,[ dba nnn=ζ . In this paper, u(k) and y(k)

are the k-th packet inter-departure time and the k-th end-to-end packet delay variation, respectively.

Of all measurements and simulation results, obtained in Section III, we use the input and the output data of 100 packets (1500 k < 1600) for coefficients determination and model validation. As an example, when =[6,6,1], coefficients of the ARX model and their standard deviations are shown in Table. 6 (the UDP case) and Table 7 (the UDP + TCP case).

Figs. 14-15 compare the measured data and the model output for =[20,20,1] in the UDP case, and in the UDP+TCP case, respectively. It is evident that in both cases, the model output )|(ˆ θky and the measured output y(k)

roughly coincide but slightly differ. This is because the measured end-to-end packet delay variation is disturbed by other unknown traffic not included in the model output

)(ˆ ky .

(a)

(b)

Fig. 14. Comparison between measured data y(k) and model output )(ˆ ky for

(a) UDP case, and (b) UDP+TCP case

(a)

(b) Fig. 15. Error between measured data y(k) and model output )(ˆ ky

for (a) UDP case, and (b) UDP+TCP case

V. RESULTS AND CONCULSIONS

We studied the Internet delay variations and proposed a model that can describe its dynamics. From our measurements, we noted a cyclic behavior for the delay despite the chaotic nature of Internet delays. We also noted the existence of sudden and enormous changes in the Internet delays (blackout), which must be taken into account to ensure stability and robustness, although some measurements tend to hide its existence. To derive our model, we employed system identification techniques and the ARX model. Results show that the model can describe the actual delay dynamics accurately. Furthermore, the model for the TCP+UDP case shows better performance compared to the model for the UDP case only.

Table 6. Coefficients and std. deviations of the ARX model (UDP case)

6a 5a 4a 3a 2a 1a0.23

10.053

0.136

0.282 0.248 0.261 coefficients

0.013

0.108 0.11

10.114 0.115 0.112 Std. Dev.

6b 5b 4b 3b 2b 1b0.01

90.011

0.008

0.0007

0.021 0.004 coefficients

0.013

0.015 0.01

60.016 0.015 0.016 Std. Dev.

Table 7. Coefficients and std. deviations of the ARX model (UDP+TCP)

6a 5a 4a 3a 2a 1a-0.11 -0.029 -0.052 0.018 0.129 0.107 coefficients 0.10

30.107 0.107 0.108 0.106 0.105 Std Dev.

6b 5b 4b 3b2b 1b

-0.03 0.028 -0.012 0.007 -0.026 0.008 coefficients 0.02 0.024 0.025 0.026 0.025 0.027 Std. Dev.

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REFERENCES

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[18] J. Danielsson and C. de Vries, “Value-at-risk and extreme returns,” Working Paper, 2001.

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