1676 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 7, JULY 2006
Modeling Node Mobility for Reliable Packet
Delivery in Mobile IP Networks
Jui-Ting Weng, Jiunn Ru Lai, and Wanjiun Liao, Senior Member, IEEE
Abstract— In this paper, we analyze node mobility for reliable
packet delivery in Mobile IP networks. In Mobile IP, packets destined to roaming nodes are intercepted by their home agents and delivered via tunneling to their Care of Addresses (CoA). A mobile node may roam across multiple subnets. At each boundary crossing, a handoff is initiated such that the CoA is updated and a new tunnel is established. We consider both basic Mobile IP handoff and smooth handoff. We find that reliable packet delivery in Mobile IP networks can be modeled as a renewal process, because the retransmission over a new tunnel after each boundary crossing is independent of the previous history. We then derive the probability distribution of boundary crossings for each successful packet, based on which the packet reliable delivery time can be obtained. Our analytical model is derived based on a general distribution of residence time in a subnet and a general distribution of successful retransmission attempts in each subnet. The results can be readily applied to any distributions for both items. We also provide numerical examples to calculate the probability distribution of boundary crossings, and conduct simulations to validate our analytical results.
Index Terms— Mobile IP, reliable packet delivery, IP mobility.
I. INTRODUCTION
M
OBILE IP [1] is the dominant standard for host mo-bility in the Internet. With Mobile IP, mobile nodes can receive packets using their home IP addresses wherever they go. The mobility service is enabled by the cooperation of mobility agents, i.e., the home agent (HA) and foreign agents (FAs), based on the operations of “binding” and “tunneling,” as shown in Fig. 1. A mobile node (MN) in the home network does not need the support of its HA. When away from home, the MN registers with its home agent a care-of-address (CoA) temporarily allocated in the foreign network. Such registration may be performed either via the foreign agent in the foreign network, or via the MN itself. In either case, the home agent will bind the received CoA with the home IP address of the roaming node, and intercepts packets from the correspondent node (CN) destined to the home IP address of the node. The intercepted packets are then sent to MN via tunneling, i.e., the original packets are encapsulated in new packets destined to the CoA of the node and sent to MN in its new location using normal IP delivery. Such address binding is also performed Manuscript received November 02, 2003; revised February 18, 2005; accepted July 24, 2005. The associate editor coordinating the review of this paper and approving it for publication was J. Hou. This paper was supported in part by the National Science Council (NSC), Taiwan, under a Center for Excellence Grant NSC94-2752-E-002-006-PAE, and in part by NSC under Grant Number NSC94-2213-E-002-047.J.-T. Weng, J. R. Lai, and W. Liao are with the Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan. Wanjiun Liao is also with the Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan (email: wjliao@ntu.edu.tw).
Digital Object Identifier 10.1109/TWC.2006.03588.
Fig. 1. System model used in the analysis.
upon each handoff (i.e., when a node moves across a network boundary). As such, mobile nodes can go anywhere and still receive packets destined to their home IP addresses.
The binding information at HA may not be updated in time during a handoff. This may cause packets in flight to the old foreign network to be lost. Once the location update information arrives at HA for address re-binding, packets can be routed to MN in the new foreign network and the reception is resumed. To shorten the service interruption suffered by the basic Mobile IP handoff, an FA-assisted smooth handoff is proposed [2]. When performing a smooth handoff to the new foreign network, FA needs to notify both HA and the old FA in the old foreign network. During the transit of each handoff, the binding information at the HA may become stale and packets are again routed to the old foreign network. But this time, the old FA will buffer these packets and tunnel them to the new FA for smooth forwarding. Therefore, packet losses incurred by the handoff can be reduced, at the expense of additional buffering and forwarding performed by the old FA.
Existing work of modeling node movements mostly focuses on PCS networks [3-5], with relatively less efforts on Mobile IP networks. Proposals in [6-7] evaluate the performance of handoff schemes based on such metrics as operation cost, packet delay and loss during a handoff. In [6], an M/M/1 queuing network model is proposed to measure the packet loss and delay of the post-registration handoff scheme. It considers the influence of the source transmission rate, link delay, and layer-2 link signaling on the performance measurement without considering node mobility. In [7], an analytical model is derived and simulation results are presented to evaluate the packet loss and packet delivery for UDP streams and the throughput for TCP streams involved in a Mobile IP smooth handoff. In [8], an analytical model is proposed to study the 1536-1276/06$20.00 c 2006 IEEE
WONG et al.: MODELING NODE MOBILITY FOR RELIABLE PACKET DELIVERY IN MOBILE IP NETWORKS 1677
impact of cell residence time, user population, session size and the MAP domain size on the location update and packet delivery cost. The analysis of supporting IP paging in Mobile IP network is then left as future work. The work in [9] points out that the probability distribution of the number of boundary crossings during a call will play a critical part in the cost analysis for PCS networks. Similarly, modeling the number of boundary crossings will play an important role for the cost analysis of IP paging service in Mobile IP networks. So far, such study has only been available for cellular networks. In this paper, we will investigate the issue of boundary crossings for Mobile IP networks.
We study the impact of cell residence time, handoff time, and packet delivery time on the number of boundary crossings (i.e., number of handoffs), and derive the probability distribu-tion funcdistribu-tion of the number of handoffs for reliable packet delivery in Mobile IP networks. Reliable packet delivery here means the packets are correctly delivered to roaming nodes, even though the wireless links are error-prone and the nodes are moving during the delivery. The total time for reliable delivery of each packet is defined to be the reliable delivery time in this paper. The exact distribution of reliable delivery time depends on the network conditions in the wired and wireless parts, the reliable packet delivery mechanism implemented at the layer-4 protocol, and residence time distribution in each cell. For example, if TCP is used, the packet loss may be recovered after several round-trip times, while with NAK-based protocols, the recovery time could be short after MN detects the loss by a sequence gap or an explicit timeout. To make our model more general, we assume a general distribution for the residence time (i.e., the total time a mobile node stays in a subnet) and for the packet retransmission time in a subnet for reliable delivery. The results can be easily extended to different situations once the actual distributions are given. Note that we focus on the per-packet behavior, and do not take into account such issues as flow control, congestion control, or error control likely to be implemented at the layer-4 protocols. The result of this paper can be extended to connections comprised of multiple packets with the consideration of the influence of layer-4 protocols.
The rest of the paper is organized as follows. In Section II, the analytical model is derived. In Section III, numerical examples are shown and simulation results are presented. Finally, the paper is concluded in Section IV.
II. ANALYSIS OFNODEMOBILITY FOR RELIABLEPACKETDELIVERY
A. System Model
In this section, we derive the probability distribution of the number of handoffs for reliable packet delivery in Mobile IP networks. The reliable delivery time T is defined as the total time for a packet to be received successfully. The packet may be transmitted several times before it can be received correctly. During a reliable delivery period T, the node may stay in a cell1, or span multiple cells. In the latter case, a handoff occurs
whenever the node moves across a cell boundary. On each 1In this paper, the terms cell and foreign network are used interchangeable.
TABLE I NOTATIONTABLE
tR(i) residence time of an MN in the ith cell, i=1, 2, 3, ...
fR(t) probability density function oftR(i), i=1, 2, 3, ...
f∗
R(t) Laplace transform offR(t)
tr residual time of an MN in the initial foreign network, i.e., the network during which a new packet first arrives
fr(t) probability density function oftr
f∗
r(t) Laplace transform offr(t)
tm(i) time interval between when a packet first arrives at the node in the ith cell and when a packet is received successfully by the node without considering node movement, i=0, 1, 2, 3, ...
fm(t) probability density function oftm(i), i=1, 2, 3, ...
f∗
m(t) Laplace transform offm(t)
th(i) handoff time accounting for the time from when MN starts a handoff to the ith cell till the first transmission arrival at MN in the ith cell, i=1, 2, 3, ...
tα(i) time taken by each individual transmission trial of the packet from CN routed to MN in the ith cell, i=0, 1, 2, 3, ...
tβ(i) time taken by each individual loss recovery operation from when MN fails to get the packet at this trial in the ith cell till the corresponding successive recovery trial transmitted by CN, i=0, 1, 2, 3, ...
Th the expected value ofth(i)
N number of handoffs experienced by an MN before the packet is delivered successfully,N=0, 1, 2, 3, 4, ...
handoff, the node needs to re-register with the home agent a new CoA in the new foreign network for address rebinding. If a handoff2occurs before the packet is successfully delivered,
a new CoA is obtained in the new network. The packet is then sent as a new copy over the new tunnel, and a series of transmissions for the new copy are conducted, irrespective of how many retries have been attempted in previous cells. Since this operation repeats after each handoff and behaves independently of the previous history, the behavior of reli-able packet delivery can be modeled as a renewal process with identically and independently distributed (iid) processing times. Note that the operation described above also applies to Mobile IP with Routing Optimization, except that in this case, the packet retransmission path is between the CN and the mobile node, not going through the tunnel between the home agent and the mobile node. In this paper, the analytical model is explained based on Mobile IP without routing optimization.
B. Analytical Model of Boundary Crossings for Reliable Packet Delivery
To analyze the handoff behavior of reliable packet delivery, some observations are made using the following terminolo-gies:
1) Residence time tR(i) means the time period for a node
staying in the ith cell.
2) Handoff time th(i) means the total time from the
handoff to the ith cell (called handoff delay to(i)) to
when the packet first arrives in the cell after the handoff3
2The description here is based on the basic Mobile IP handoff. We will
show that this model is also applicable to the FA-assisted smooth handoff in a later section
3A packet may not arrive at the new cell right after the finish of the handoff
process. The delay duration may depend on the handoff scheme, the layer-4 protocol, and the distance between CN and MN. The delivery deferred time here accounts for all these delays.
1678 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 7, JULY 2006
(a)
(b)
Fig. 2. Handoff condition: a)tR(i) ≥ th(i) + tm(i); b) tR(i) < th(i) +
tm(i).
(called delivery deferred time). The handoff delay here accounts for the delay that a new CoA is obtained in the new FN and address rebinding is performed at HA. The delivery deferred time refers to the time from when MN moves into the ith cell till the first retransmission arrival at MN in the ith cell.
3) Retransmission time tm(i) means the transmission time
of the packet in the ith cell without considering node movement (i.e., treating the node as a fixed host). When a packet is successfully delivered to the node in a cell, say, i, the cell residence time is larger than or equal to the handoff time plus the retransmission time, i.e., tR(i) ≥ th(i)+
tm(i) ; when a handoff occurs before the reliable delivery is
done, the residence time is small than the handoff time plus the retransmission time, i.e., tR(i) < th(i) + tm(i) . Fig. 2
depicts these two cases.
Fig. 3 shows the timing diagram for node movements in a reliable delivery time T based on this concept, where t denotes the time when the packet arrives at the initial foreign network (i.e., F N0), and ti indicates the time for the handoff
to foreign network F Ni; trdenotes the residual time for MN
staying in the initial foreign network F N0. According to the
random observer probability from the renewal theory [10], the distribution of the residual time can be derived as follows. Let
fr(t) denote the probability density function of tr, and fr∗(s)
denote the Laplace transform of fr(t). Thus, we have
fr(t) = λr ∞ t fR(τ)dτ = λr(1 − FR(t)), fr∗(s) = λr×(1 − f ∗ R(s)) s ,
where fR(τ) is the probability density function of tR, the
residence time of the MN in F N0, and λr is the inverse of
the mean residual time in F N0.
For a successful delivery in F N0, we have tm(0) ≤ tr; for
a successful delivery in any other cell, say, F Ni, we have
[th(i) + tm(i)] ≤ tR(i) , tm(0) > tr,
[th(j) + tm(j)] > tR(j), j = 1, . . . , i − 1,
because the retransmission attempts in previous cells all fail. Let the reliable delivery time T span over N handoffs as
Fig. 3. Timing diagram forN handoffs in a packet delivery time. shown in Fig. 3. This means that the retransmission time plus the handoff time for a packet in a cell is larger than the residence time of the MN in the cell, except for the last cell, i.e., F NN, where the packet retransmission time plus the
handoff time is less than or equal to the residence time, i.e.,
tm(0) > tr, [th(i) + tm(i)] > tR(i) for i = 1, 2, . . . , N − 1,
and [th(N) + tm(N)] ≤ tR(N). During the stay in each cell,
the packet is retried until a handoff occurs, when the tunnel will be reestablished and a new retransmission process will start while ignoring the previous retries (i.e., a renewal process starts). This operation repeats (i.e., probabilistically the same) in each cell until the packet is correctly received in subnet
F NN , when the packet will be successfully delivered.
Let N is the number of handoffs during the reliable delivery time T , N = 0, 1, 2 . . . . The probability distribution of N can be expressed as follows. P r[N = 0] = P r[tm(0) ≤ tr]. (1) P r[N = n] = P r[tm(0) > tr] × n−1 i=1
P r[tm(i) + th(i) > tR(i)]
× P r[tm(n) + th(n) ≤ tR(n)], n = 1, 2, . . .(2)
Based on (1) and (2), the random variable T can be expressed as follows. T = (tm(0)|tm(0) ≤ tr)P r(N = 0) + ∞ n=1 ((tr|tm(0) > tr) + n−1 i=1
(tR(i)|tm(i) + th(i) > tR(i)) + th(n)
+(tm(n)|tm(n) + th(n) ≤ tR(n)))
×P r(N = n). (3)
The first term in (3) corresponds to no handoffs in time
T , and the second term corresponds to the reliable delivery
time T spanning over multiple subnets. Since it is a renewal after each handoff, the time spent in each cell is equal to the corresponding residence time under the condition that a handoff occurs before the packet is received correctly, except for the last cell, in which the time spent is the handoff time plus the retransmission time for the successful delivery. Thus, the sub-terms inside the second term further correspond to (i)
1684 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 7, JULY 2006
(a)
(b)
Fig. 9. The impact ofThon reliable delivery time E[T]: a)tR; b)tM. - 18 sec, and tm is a Gamma distribution with a mean of 1
sec and α = 2. In Fig. 9 (b), the analytical curves of E[T] are plotted as a function of tm with different settings of handoff
time Th. In this figure, tRis a second order Erlang distribution
with a mean of 10 sec, and tmis a Gamma distribution with
α = 2 and λm ranging over 1 - 9 sec. We see that a smaller
tR or a larger tm results in a larger E[T], as expected. The
value of E[T ] increases as Th increases. Fig. 9 also verifies
the analytical result via simulation. It can be observed that all sets of curves match very well, showing the accuracy of our analytical model.
IV. CONCLUSION
In this paper, we have modeled the behavior of node move-ments for reliable packet delivery in Mobile IP networks. The probability distribution of the number of boundary crossings for reliable packet delivery is derived, based on which the distribution and the mean of the packet delivery time can be obtained. To make the analytical model more general, the derivation assumes general distributions for both residence time and local retransmission attempts in each subnet. The re-sults can be readily applied to any actual distributions for both items. We also provide numerical examples to demonstrate how to use our model to calculate the probability distribution of boundary crossings, given the distributions of residence time and local retransmission attempts.
In the future, we will further model the behavior of reliable multicast packet delivery over Mobile IP networks based on the derived analytical result.
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Jui-Ting Weng received the B.S. and MS degrees
in Electrical Engineering from National Taiwan University, Taipei, Taiwan, in 2003 and 2005, re-spectively. His research interests include wireless communication and QoS issues in ad hoc networks.
Jiuun-Ru Lai received the B.S. and PhD degrees in Electrical Engineering
from National Taiwan University, Taiwan, in 1995 and 2004, respectively. He served as a post doctor in Department of Electrical Engineering, National Taiwan University, Taiwan from 2004 to June 2005. He is now joining the VoIP pilot project funded by Intel and National Taiwan University Hospital as a system engineer. His research interests include protocol design and analysis of wireless communications and QoS issues in multimedia networks.
Wanjiun Liao received the BS and MS degrees
from National Chiao Tung University, Taiwan, in 1990 and 1992, respectively, and the Ph.D. degree in Electrical Engineering from the University of Southern California, Los Angeles, California, USA, in 1997. She joined the Department of Electrical Engineering, National Taiwan University (NTU), Taipei, Taiwan, as an Assistant Professor in 1997. Since August 2005, she has been a full Professor. Her research interests include wireless networks, multimedia networks, and broadband access net-works. Dr. Liao is actively involved in the international research community. She is currently an Associate Editor of IEEE Transactions on Wireless Communications and IEEE Transactions on Multimedia. Dr. Liao has received many research awards. She was a recipient of the Outstanding Research Paper Award in Electrical Engineering at the University of Southern California in 1997. Two papers she co-authored with her students received the Best Student Paper Award of the First IEEE International Conferences on Multimedia and Expo (ICME) in 2000, and the Best Paper Award of the First International Conference on Communication, Circuits and Systems in 2002. Dr. Liao was elected as one of Ten Distinguished Young Women in Taiwan in 2000 and was listed in the Marquis Who’s Who in 2001-2003, and the Contemporary Who’s Who in 2003.
![Fig. 9. The impact of T h on reliable delivery time E[T]: a) t R ; b) t M .](https://thumb-ap.123doks.com/thumbv2/9libinfo/8822410.232648/4.850.94.364.75.496/fig-impact-t-reliable-delivery-time-e-t.webp)
