Rate Adaptation Schemes in Networks with Mobile ... - Semantic Scholar

Rate Adaptation Schemes in Networks with Mobile Hosts B. R. Badrinath Anup Kumar Talukdar Department of Computer Science Department of Computer Science Rutgers University Rutgers University New Brunswick, NJ 08903 New Brunswick, NJ 08903 E-mail : [email protected] E-mail : [email protected] Arup Acharya C&C Research Labs, NEC USA Princeton, NJ 08540 E-mail : [email protected] Abstract This paper considers the problem of hando management in an Integrated Services Packet Network supporting mobile hosts. In such a network, links may become overloaded due to a high concentration of mobile hosts within a given cell. As a result, the required Quality of Service guarantees cannot be provided to all ows in that cell. However, there exists adaptive applications which can operate over a wide range of available bandwidth. Thus, it may be possible to overcome the link overload condition by reducing the bandwidth of individual ows, which we call rate adaptation. The two most important properties of a rate adaptation scheme are its network overhead and its fairness property. Rate adaptation schemes which ensure certain fairness properties, such as maxmin optimality criteria, have very high network overhead. Therefore, these schemes are not suitable for a highly mobile environment where rate adaptation may have to be invoked frequently. In this paper, we investigate the tradeo between the network overhead and the fairness property of rate adaptation in a mobile environment. We rst characterize the fairness property of rate adaptation by several measurable parameters. We then describe two rate adaptation schemes, one of which has very low network overhead but is `unfair', while the other scheme is `fair' but has very high network overhead. Finally we propose a new rate adaptation scheme which reconciles the two con icting properties. Results of simulation experiments comparing the performances of the three rate adaptation schemes are presented.

KEYWORDS: Mobility, Quality of Service, Rate

 This

research work was supported in part by DARPA under contract numbers DAAH04-95-1-0596 and DAAG55-97-1-0322, NSF grant numbers CCR 95-09620, IRIS 95-09816 and Sponsors of WINLAB. To Appear in the Proceedings of the ACM/IEEE MobiCom 1998 Conference.

Adaptation, Fairness, Network Performance, Hando Management 1 Introduction The portable computers such as laptops and palmtops are becoming easily available now-a-days due to the signi cant progress of computing technology. Simultaneously, the progress of wireless digital communication has made it possible to connect portable computers with the xed network. This has led to an intensive research in the area of Mobile Computing to provide mobile users access to an inter network. There are many schemes in the literature that have focussed on the problem of maintaining connectivity at the network and transport layer in spite of the mobility of the mobile hosts[2, 3]. Also, there have been several proposals for supporting real-time applications in an Integrated Services Packet Network (ISPN). Typical applications that require real-time services include audio library, image browsing, video conferencing and video-on-demand. These multimedia applications require a bound, which may be absolute or statistical, on the delivery delay of each packet. Clark et. al.[8] have described an architecture for an ISPN that supports real-time trac. As portable computers become more powerful and the accessibility of a xed network from a mobile host becomes easier, the number of mobile users will grow and additionally the mobile users will demand the same real-time services available to xed hosts. Mobility of hosts has a signi cant impact on the QoS parameters of a real-time application. The existing system architecture[8] for real-time services in a network with xed hosts is not adequate for supporting mobile hosts. To mitigate the impacts of mobility on the real-time services to mobile users, several new system architectures have been proposed by Talukdar et. al.[21, 22], Lu et. al.[14] and Lee[13]. In this paper, we address the problems of hando management in a multimedia network with mobile hosts. In such a network, certain links may become overloaded when a large number of mobile hosts enter into a cell and the bandwidth of the link is not sucient to provide the required throughput of all ows simultaneously. This problem may also arise in a link sharing environment[10], where multiple agencies, protocol families, or trac types share the bandwidth of a common link. In such a system, the available bandwidth to

a particular service class may vary over time depending on the user load in other service classes. One way to overcome the overload condition of the link is to drop a sucient number of ows so that the total bandwidth requirement of the remaining ows is less than or equal to the link bandwidth (usually, the incoming ow, whose entry into the link caused the link overload, is dropped). However many applications are adaptive in nature and they can operate over a wide range of bandwidth. For example, in the wireless communication environment, recently developed hardware for video coding can adaptively deliver digital video at rates between 60K bits/sec and 600K bits/sec [4]. Also, to support heterogeneous receivers, use of layered media streams has been suggested for real-time multimedia transmissions [9, 12, 15, 19]. In this model, the multimedia data source disseminates multiple levels of quality across multiple network channels and a receiver can adapt its reception rate by adjusting the number of layers it receives. There has been several proposals for layered video compressions and layered transmission systems [16, 6]. Therefore, in such a network, it may be possible to overcome the link overload condition by reducing the bandwidth of individual ows, which we call rate adaptation. The two important properties of a rate adaptation scheme are: the fairness criteria, which indicates which ows are aected and how they are aected, and message overhead required to inform the senders and receivers of their new rates. Rate adaptation schemes which distributes the link bandwidth to all ows in a fair way have usually high message overhead, because the rates of a large number of ows may be changed. In this paper, we investigate the tradeo between the message overhead and the fairness property of rate adaptation schemes in a mobile network. The paper is organized as follows. In Section 2 we describe the eects of mobility on the real-time applications and the rate adaptation schemes. In Section 3, we describe the related works. In Section 4, we describe the mobile network model we consider in this paper and discuss the fairness issue of rate adaptation in this model; we also characterize the fairness property by several parameters. In Section 5 we formally describe the problem of rate adaptation; then we describe three rate adaptation schemes and illustrate their dierences using an example. In Section 6, we provide the details of simulation experiments and compare the performances of the three rate adaptation schemes. In Section 7 we conclude mentioning future work.

2 Eects of Mobility The main QoS parameters for real-time services are packet delay, packet loss rate, delay jitter and throughput. To provide real-time services, a network is designed to provide suf cient guarantees on these QoS parameters. Mobility of a host has a signi cant impact on these QoS parameters. When a mobile host moves from one location to another with an active ow, the data ow path changes. As a result the propagation delay of packets may change. The congestion delay at the routers along the new path may be dierent from that in the previous path. If the new cell into which the mobile host moves, is overcrowded, the available bandwidth in the link may not be sucient to provide the throughput it was receiving at the previous cell. In addition, the mobile user may suer temporary disruption of service during hando while the ow is teared down along the old path and it is established along the new path. Therefore, the mobile users may have to adapt to these

changes as they move with their active ows. The possible impacts of mobility on a ow may be change in throughput, change in end-to-end delay bound and delay jitter bound of packets. There are two types of real-time applications: intolerant and tolerant. Intolerant applications require guaranteed service which provides an absolute bound on the delivery delay of each packet. Tolerant applications have the ability to adapt to occasional variations (up to a maximum limit depending on the application) in the delay bounds of the packets; they can be served by predictive service, which can provide a fairly reliable bounds in the delivery delay of the packets. When the bandwidth demand on a link increases, it may be possible to sustain the throughput levels of the ows at the expense of increased delays. But in a mobile environment, the number of mobile hosts visiting a cell may vary widely. Thus, even for the predictive service, the delay bounds may exceed the tolerable limit. Under this situation, delay bounds can be restored if the bandwidth requirements of the ows are reduced. However, in some extreme cases, some ows to the mobile users may have to be dropped if the minimum bandwidth requirements of all ows cannot be satis ed[13, 14]. If a cell is currently overloaded and some mobile host moves out of a cell or terminates its ow, it may be possible to increase the throughput of the remaining ows so that the utilization of the link is maximized. Rate adaptation has two functional components: rate computation, by which the new rates for the ows are computed by the router of the link and rate noti cation, i.e., informing the sender and receiver of a ow of the new computed rate by sending messages. Thus the message overhead is proportional to the number of ows whose rates are changed. In a network with mobile hosts, rate adaptation may have to be invoked frequently due to frequent handos by the mobile hosts and hence the message overhead may be extremely high. Thus it is necessary to keep the number of ows aected by a rate adaptation as small as possible.

3 Related Work The problem of allocating the available bandwidth of a link to a set of existing ows has been studied well in the literature. Many of these research have been done in the context of rate control for Available Bit Rate(ABR) trac in an ATM network. These works have focused on the eciency and fairness of the rate allocation scheme. Charny [7], Abraham et. al.[1] and Tsang et. al.[23] have proposed distributed algorithms that ensures max-min fairness[5, 11, 17, 18]. These algorithms compute fair rates for all ows over the entire network. In a mobile environment, Lu et. al.[14] have used the distributed rate allocation algorithm proposed by Charny[7] to reallocate the link bandwidth after hando by a mobile host and ow termination. In this work a threshold based activation of rate reallocation has been proposed to reduce the overhead of rate reallocation. However, we observe that, the message overheads of rate reallocation schemes which are `fair' (e.g. max-min fair) are inherently high, because the rates of many ows may change to ensure the fairness criteria. There has not been any investigation into the overall network overhead of max-min fair rate allocation in a network with mobile hosts where rate adaptation is invoked frequently. We like to mention that, investigating the tradeo between the message overhead and fairness of rate adaptation schemes in the context of a xed network is a signi cant problem. However, we observe that, this problem is more severe in a mobile network in which rate adaptations are

invoked more frequently. Therefore, in this paper, we study this problem in the context of a mobile network.

4 Fairness Criteria in a Network with Mobile Hosts In this section, we rst describe the network model and then we discuss the fairness criteria in the mobile environment. 4.1 Network Model We consider a cellular network architecture where a geographical area is divided into a number of regions, called cell. Each cell is covered by a base station which provides wireless network access to the mobile hosts in that cell. Base stations are connected to the wired backbone network. The bandwidth of an wired link in the backbone network is much higher than the bandwidth of an wireless link. Thus we assume that, when a large number of mobile hosts enter into a single cell, only the wireless link of the cell can become overloaded; wired links have enough capacity to satisfy any arbitrary amount bandwidth requirement. With this simplifying assumption, we can avoid the complexities of the distributed rate allocation problem. However, if the wired links have limited bandwidth, we can use the rate reallocation schemes discussed in e.g. [7, 14] combined with the rate adaptation schemes described later in this paper. We also assume that, the base stations have sucient computing power and therefore it is more important to reduce network overhead (possibly) at the expense of computations at the base stations. This work is based on the fact that, applications requiring QoS guarantees are adaptive in nature and can operate over a wide range of bandwidth. In our model, each application has an associated discrete set of throughput levels and it can operate at any of those bandwidth; higher throughput level will have a better QoS. The sender and the receiver of a ow should know in advance the throughput level of operation so that they can setup their transmission and reception functionalities accordingly. Thus, when the base station changes the throughput of a ow from one level to another, it must communicate the new throughput value to the sender and the receiver by sending messages. In this paper we consider this message overhead to be a principal cost parameter of rate adaptation schemes. This overhead is directly proportional to the number of ows whose rates are changed. Rate adaptation may have to be initiated under three circumstances:  Hand-in: A mobile host with an active ow moves into a cell and the wireless link bandwidth is not suf cient to provide the current throughput level of all

ows.  Hand-out: The wireless link of a cell is currently overloaded and some ows are operating at a level which is below their maximum throughput requirement. If in this situation a mobile host with an open ow moves out of the cell, the excess available bandwidth may be used to upgrade the throughput of some ows. This will improve the link utilization.  Termination: When a ow terminates some excess bandwidth becomes available. This excess bandwidth can be allocated to some of the existing ows which are not receiving their maximum bandwidth levels and the link utilization can be improved.

Note that, we do not invoke rate adaptation to admit a new

ow in an overloaded cell. In other words, no new ow is admitted in an overloaded cell.

4.2 Mobility, Fairness and Network Overhead In a xed network, max-min optimality criteria has been used for rate allocation[7]. The details of this fairness criteria can be found in [5, 7, 11, 17, 18]. A rate allocation scheme satisfying this fairness criteria allocates rates to the

ows in the following way. We rst consider all bottleneck links, i.e. the link with the smallest bandwidth available per

ow. The total bandwidth of each of these links are shared equally among all ows passing through that link. Then these ows are removed from the network and the available bandwidths of the links are reduced by the bandwidth consumed by the removed ows. Then the next level bottleneck links are identi ed and the process is repeated. This process is continued until all ows are assigned their rates. In a mobile network, Lu et. al.[14] have used this procedure for dynamic rate adaptation when mobile users move from one location to another. In this scheme, all ows are rst assigned their minimum throughput requirement. Then the excess available bandwidth is allocated to all ows according to the above criteria. This procedure can be easily adapted to the network model we consider in this paper. However, since this procedure ensures fairness among all ows, it will potentially change the throughput of many

ows each time this is invoked. This may generate many messages in the network. Thus although it is fair, the network overhead may be very high. In the above rate adaptation scheme, the available bandwidth is allocated to the ows fairly every time a hando occurs or a ow terminates; thus fairness is ensured at all times among the ows within a cell. However, we observe that, a mobile host may visit many locations during the lifetime of its ow and it may receive dierent throughput at dierent locations depending on the number of users at those locations. Thus, the average bandwidth obtained by a ow over its entire duration depends on the locations it has visited. It is quite possible that, although the above rate adaptation scheme always ensures fairness among all

ows within a cell, it does not ensure fairness among ows if fairness is evaluated over longer duration. For example, let us de ne the aggregate quality of a ow to be the overall quality of service (we will shortly give a precise de nition) it has received over its duration. Then we can characterize the fairness property of a rate allocation scheme in terms of its impact on the aggregate quality received by a ow. Let S be the set of all ows in the network and let var(X ) denote the variance of the random variable X . We use the following notations for the dierent parameters of a ow:

 biavg = Ti 1

Z Ti

Ti

0+

Ti0

bi (t)dt, where

Ti0 = starting time of ow i Ti = duration of the ow i bi (t) = the bandwidth received by ow i at time t.  bmax i = maximum bandwidth requirement of ow i.

The fairness property of a rate allocation scheme can be characterized by the following parameters: avg

i )  var average bw: It is de ned as the variance of ( bbmax i over all ows i 2 S .

i t ) over all ows i 2 S .  var bw var: Variance of var( bbmax i ( )

This is computed in two steps: 1. Compute Xi = variance of the normalized bandi(t) ) width of ow i over its duration = var( bbmax i 2. var bw var = var(Xi ) over the set of ows S .  mean bw change: Mean of bandwidth change rate of all

ows, where bandwidth change rate of a ow is de ned as the average number of times the bandwidth level of the ow is changed per second over its lifetime. In this paper we measure the network overhead of a rate adaptation scheme in terms of the following two parameters:  time count: It is the average number of ows whose rates are changed per second.  hando count: It is the average number of ows whose rates are changed per hando. To compute this average, we count only those handos which invoke rate adaptation.

5 Rate Adaptation Schemes In this section, rst we formally describe the problem of rate adaptation in our network model. Then we describe a rate adaptation scheme minimumadaptation which has a very low network overhead, but is unfair. Next we present the rate adaptation scheme fair adaptation. In this scheme, all ows are rst allocated their minimum throughput requirement. Then it allocates the excess available bandwidth equally among all ows. This scheme has high network overhead. Then we describe a simple modi cation of the minimum adaptation scheme which we call average-fair adaptation. This scheme has better fairness characteristics than minimum adaptation but less network overhead than fair adaptation. 5.1 Rate Adaptation Problem Suppose, a cell currently has an active set of ows S = fi0 ; i1 ; :::;in?1 g. A ow i can operate at any of the ji bandwidth levels l0 ; l1 ; :::;lji ?1 , where l0 > l1 > ::: > lji ?1 . Assume that, the ow fi is currently operating at level lki , where 0  ki < ji . These bandwidth levels are speci ed by the application and they represent either the worst case bandwidth requirement or the average bandwidth requirement of a ow at each level of operation. A rate adaptation scheme consists of two actions: degrade and upgrade. When an existing ow enters into the cell from another cell, the total bandwidth requirement of all ows (including the incoming ow) operating at their current level may exceed the link capacity; we say that the link is overloaded. In this situation, if the total minimum bandwidth requirements of all ows exceed the link capacity, the incoming ow is dropped; otherwise, the link overload condition is resolved by degrade, i.e. by reducing the bandwidth levels of the

ows. When the bandwidth of a ow i is reduced by ri , we say that ow i has a reduction ri . Thus, the problem of degrade can be formally described as follows:

P

P

Let b be the bandwidthi de cit in a link with capacity C , i.e. b = i2S lki ? C , and C  i2S ljii ?1 . Find a minimal subset S 0  S0 and an associated set of reductions R = fri j i 2 S ^ ow i is reduced by ri g, such that, i2S0 ri  b.

P

Algorithm min-handin

Insert ow i into S ; Compute r = currently available excess bandwidth = C ? lkj j ;

X

if (r  0) then

j2S

Increase the bandwidth level of ow i as much as possible, i.e. set ki = j , such that, lji  r ^ (j = 0 _ lji ?1 > r); Insert ow i into avail list and degraded list; else min-degrade(?r);

endif End min-handin

Figure 1: Algorithm min-handin When the link is overloaded and a ow moves out of the cell or terminates, the bandwidth levels of some ows operating at below their maximum levels can be increased by upgrade. When the bandwidth of a ow i is increased by ri , we say that the ow i has a raise ri . Thus, the problem of upgrade can be described as follows: Let b be the excess bandwidth in a link with capacity C , i.e. b = C ? i2S lki i . Find a maximal subset S 0  S and an associated set of raises R = fri j i 2 S 0 ^ ri is the raise of ow ig, such that i2S0 ri  b. Note that, in the above formalizations, although it is intended to maintain the link utilization as high as possible, no optimality criteria, with respect to either fairness or network overhead, has been speci ed for the subset S 0 . Given a set of ows S and a value b, dierent upgrade or degrade 0 schemes may compute dierent subsets S of S and the corresponding sets of raises and reductions. We are interested in those adaptation schemes which satisfy certain fairness criteria and constraints on network overhead.

P

P

5.2 Minimum Adaptation In this rate adaptation scheme, upgrade and degrade are done in such a way that, the number of ows whose bandwidth levels are changed, is minimized. In the following, we rst describe the scheme and then discuss its properties. 5.2.1 Data Structures and Algorithms For each ow i, we de ne two quantities, availability ai and demand di as follows:  ai = lki i ? ljii ?1 . It is the maximum amount of bandwidth the ow i can release without being dropped.  di = l0i ? lki i . It is the maximum amount of additional bandwidth the ow i may request (to improve its QoS). For each link, the router (base station) maintains two data structures: avail list and degraded list. In the avail list, the

ows in the link are kept sorted in the non-increasing order of their availability. The ows operating at their minimum level of bandwidth (i.e. ai = 0) are kept sorted in non-decreasing order of their current bandwidth. In the

Algorithm min-degrade(r)

/* r = bandwidth de cit in the cell */ Insert ow i into avail list and degraded list; sum = 0; p = 0; while (p < avail list count) do q = avail list[p]; if (kq == jq ? 1) then break;

Algorithm min-handout

Delete ow i from S , avail list and degraded list; if (degraded list is non-empty) then min-upgrade;

endif End min-handout

endif

sum = sum + lkqq ? ljqq ?1 ; if (sum  r) then break; endif

p = p + 1;

endwhile if (sum < r) then

Delete ow i from S and drop the ow i; Delete ow i from avail list and degraded list;

else

p1 = 0; q = avail list[p]; s = kq + 1; sum = sum ? (lkqq ? ljqq ?1 ); while (s < jq ) do if (sum + lkqq ? lsq  r) then break; endif

s = s + 1; endwhile kq = s; p1 = 0; while (p1 < p) do q = avail list[p1]; kq = jq ? 1; Delete ow q from avail list and degraded list; Insert ow q into avail list and degraded list; p1 = p1 + 1;

endwhile endif End min-degrade

Figure 2: Algorithm min-degrade degraded list the ows operating at below their maximum bandwidth levels are kept sorted in non-increasing order of their demand. The size of avail list and degraded list (in number of ows in the list) are maintained in avail list count and degraded list count. When an existing ow i enters into the cell from another cell, the algorithm min-handin (Figure 1) is executed. The algorithm min-handin works as follows. First it checks, if the currently available bandwidth of the link is enough to provide the minimum bandwidth required by ow i. If that is possible, ow i is allocated as much bandwidth as possible. Otherwise, degrade is performed by the algorithm min-degrade (Figure 2). Algorithm min-degrade rst checks, if the minimum bandwidth requirements of all ows (including ow i) can be provided by the link. If not, ow i is dropped. Otherwise, it computes the bandwidth de cit b. Then the ows in the avail list are reduced to their minimum bandwidth level in the non-increasing order of their availability until there is no bandwidth de cit.

Figure 3: Algorithm min-handout When a ow i moves out of a cell or terminates, the algorithm min-handout (Figure 3) is executed. The algorithm min-handout rst checks, if the link is overloaded, i.e. there are some ows operating at below their maximum bandwidth levels. If so, the algorithm min-upgrade (Figure 4) is executed. Algorithm min-upgrade computes the excess available bandwidth of the link. Then it increases the bandwidth level of the ows in the degraded list as much as possible in the non-increasing order of their demand. The details of the algorithms are as follows: Algorithm min-upgrade

X

Compute r = excess available bandwidth in the cell = C ? lkj j ; j2S

p = 0; while (r > 0) do q = degraded list[p]; s = kq ; for (p1 =q 0; p1q< kq ; p1 = p1 + 1) if ((lp1 ? lkq )  r) then r = r ? (lpq1 ? lkqq ); kq = p1; Re-insert ow q into avail list and degraded list; break;

endif endfor

p = p + 1;

if (p == degraded break; endif endwhile End min-upgrade

list count) then

Figure 4: Algorithm min-upgrade

5.2.2 Properties The above algorithms try to minimize the number of ows whose rates are changed. Thus, the network overhead of this scheme will be low. However, this bandwidth adaptation scheme can be characterized as \unfair" because, only a minimum number of ows are aected by the handos. It may be possible that, some ows are aected more frequently than other ows. Thus, some ows will experience frequent change of its bandwidth level, whereas some ows may receive nearly constant bandwidth level during their lifetime. Moreover, some ows may get their maximum bandwidth

Algorithm fair-handin

P

Compute r = available bandwidth = C ? q2S lkqq ; p = 0; while (p < ji ) do if (r  lpi ) then ki = p; Insert ow i into S ; break; else p = p + 1; endif endwhile if (p == ji ) then

Insert i into S ; Compute r = C ? if (r < 0) then

X lq q2S

jq ?1 ;

Delete i from S ; Drop ow i;

else adjust; endif

End fair-handin

Algorithm fair-handout

P

Delete ow i from S ; Compute max demand = q2S l0q ; if (max demand > C ) then adjust;

endif End fair-handout

Figure 5: Algorithms fair-handin and fair-handout

Algorithm adjust Set 8q2S kq = jq ? 1; S1 = ;; for all (q 2 S ) if (kq 0) then

S1 = S1 [ fqg;

endif endfor while (j S1

r=C?

jX > 0) do q2S

lkqq ;

average increment = r= j S1 j; change count = 0; for all (q 2 S1 ) p = 0; q q while ((lp ? lkq ) > average increment) do p = p + 1; endwhile if (p < kq ) then kq = p; change count = change count + 1;

endif endfor if (change

count == 0) then Find q 2 S1 such that, 8s2S1 ((lkqq ?1 ? lkqq )  (lkss ?1 ? lkss )); S1 = S1 ? fqg;

endif endwhile End adjust

levels, whereas some may get their minimum levels during their lifetime.

Figure 6: Algorithm adjust

5.3 Fair Adaptation In this rate adaptation scheme, we try to distribute the impact of a hando to all ows in a `fair' way. There are several possible fairness criteria. In this scheme we use the following fairness criteria: After allocating the minimum levels of bandwidth to each ow, the excess available bandwidth of the link is `equally' distributed to all ows; however, a ow can get at most its maximum bandwidth requirement.

5.3.2 Properties The above fair adjustment scheme ensures a fair rate allocation as mentioned in Section 4. Although, it is dicult to prove any result on the number of ows whose rates are changed by this scheme, it can be observed that the average number of ows adjusted can be considerably higher than that in the minimum adaptation scheme. Thus the message overhead due to rate adaptation can be higher than the network overhead in minimum adaptation scheme.

5.3.1 Algorithms In this scheme, the upgrade and degrade are performed by the same algorithm, adjust, which allocates the link bandwidth to the ows according to the above fairness criteria. When an existing ow i moves into the cell from another cell, the algorithm fair-handin is executed. Algorithm fair-handin rst checks, if the currently available bandwidth of the link is sucient to satisfy the minimum bandwidth requirement of ow i. If so, ow i is allocated as much bandwidth as possible. Otherwise, the algorithm adjust is executed. When a ow i moves out of the cell or terminates, the algorithm fair-handout is executed. Algorithm fair-handout, rst checks if the link is overloaded, i.e. some ows are operating at below their maximum bandwidth level. If so, it executes the algorithm adjust. The algorithms fair-handin, fair-handout and adjust are described in Figures 5 and 6.

5.4 Average-fair Adaptation In this rate adaptation scheme, we use the average bandwidth of the currently active ows (till the current time, say t), in a cell to determine which ows should be upgraded or degraded when a ow hando occurs or a ow terminates. This scheme is almost similar to the minimum adaptation scheme, except that, the avail list and the degraded list are kept sorted on a composite key. The primary key is the relative average bandwidth ci of ow i obtained by the ow till the current time and de ned as: i cavg i = bavg i (t)=l0 , where bi (t)= mean bandwidth obtained by ow i till time t Z t bi (t1 )dt1 . = (t?1T 0 ) i Ti0

(Ti0 = starting time of ow i)

The secondary key is the same as the key in the avail list and degraded list in the minimum adaptation scheme. The avail list is kept sorted in the non-increasing order of the relative average bandwidth and non-increasing order of availability. The degraded list is kept sorted in the non-decreasing order of relative average bandwidth and non-increasing order of demand. The algorithms for the degrade and upgrade actions, average-degrade and average-upgrade respectively, are obtained by adding the following two steps at the beginning of the min-degrade and min-upgrade algorithms in minimum adaptation scheme: j 1. For each ow j 2 S , compute cj = bavg j (t)=l0 . 2. Sort the avail list and degraded list in the order as described above. In the average-upgrade and average-degrade algorithms, an insertion of a ow into the avail list and degraded list is always done maintaining the sorted order described above. When the link is overloaded, the algorithm averagedegrade selects a sucient number of ows from the avail list in the non-increasing order of their relative average bandwidth. Then, the bandwidth levels of the selected

ows are reduced to their lowest level of operation. Similarly, when some excess bandwidth becomes available on the link, the algorithm average-upgrade selects a sucient number of ows from the degraded list in the non-decreasing order of their relative average bandwidth and the bandwidth of the selected ows are increased to the maximum possible level. Thus, these algorithms are similar to the algorithms min-degrade and min-upgrade with respect to the policy of bandwidth reduction and increase. Therefore, we expect that, the number of ows whose bandwidth levels are changed will be small compared to that in fair adaptation. Since the algorithm average-degrade (averageupgrade) always selects the ows with larger (smaller, respectively) relative average bandwidth rst, the overall bandwidth allocation to the ows over a long duration will have better fairness characteristics than the bandwidth allocation of the minimum adaptation. Simulation results, presented in Section 6, support these observations.

5.5 An Example We illustrate the operations of the three rate adaptation schemes by considering an example. In this example, the capacity, C , of the wireless link in a cell is 2048Kbps. The ows are homogeneous, i.e., they have the same bandwidth levels of operation consisting of ve levels: (256Kbps, 224Kbps, 192Kbps, 160Kbps, 128Kbps). At a certain instant of time t, assume that the current bandwidth levels and the average bandwidths of the ows which are active in the cell are as follows: Flow Bandwidth level Average bandwidth i0 224Kbps 220Kbps i1 224Kbps 240Kbps i2 224Kbps 200Kbps i3 224Kbps 220Kbps i4 192Kbps 220Kbps i5 192Kbps 220Kbps i6 192Kbps 245Kbps i7 192Kbps 250Kbps i8 192Kbps 245Kbps i9 128Kbps 250Kbps

Let, the ow i10 enters into the cell from an adjacent cell at time t. The bandwidth level of ow i10 at time t is 256Kbps and its average bandwidth till time t is 240Kbps. As a result, the link becomes overloaded. The three adaptation schemes work as follows:  Minimum adaptation: The bandwidth de cit is r = (224 + 224 + 224 + 224 + 192 + 192 + 192 + 192 + 192 + 256)Kbps ? 2048Kbps = 192Kbps. The content of the avail list is : (i10 ; i0 ; i1 ; i2 ; i3 ; i4 ; i5 ; i6 ; i7 ; i8 ; i9 ). Note that, this list is sorted by availability. The min-degrade algorithm reduces the bandwidth levels of the ows i10 and i0 . After the adaptation, the bandwidth levels of the ows i10 and i0 are: i10 : bandwidth level = 128Kbps i0 : bandwidth level = 160Kbps The bandwidth levels of all other ows remains unchanged. After the adaptation, avail list = (i1 ; i2 ; i3 ; i4 ; i5 ; i6 ; i7 ; i8 ; i0 ; i9 ; i10 ). Number of ows whose bandwidth changed = 2.  Fair adaptation: After ow i10 enters, the excess available bandwidth in the link after allocating the minimum bandwidth level to each ow is r = 2048Kbps ? 11  128Kbps = 640Kbps. Average increment for each ow = r=11 = 58.18Kbps. After the rst iteration of the outer while loop of the algorithm adjust (Fig. 6), each of the 11 ows have bandwidth level at 160Kbps. After the second and third iterations of the while loop, the bandwidth levels of the ows do not change (only the size of the set S1 decrements by 2). After the fourth iteration of this while loop, the bandwidth assignments are as follows: Flow Bandwidth level i0 192Kbps i1 192Kbps i2 192Kbps i3 192Kbps i4 192Kbps i5 192Kbps i6 192Kbps i7 192Kbps i8 192Kbps i9 160Kbps i10 160Kbps Number of ows whose bandwidth changed = 6.  Average-fair adaptation: In this scheme, the average bandwidth of the ows are used to select which

ows will be degraded. The content of the avail list is (i7 ; i6 ; i8 ; i10 ; i1 ; i0 ; i3 ; i4 ; i5 ; i2 ; i9 ). Note that, this list is sorted by the composite key (See Section 5.4). The bandwidth de cit is r = (224 + 224 + 224 + 224 + 192 + 192 + 192 + 192 + 192 + 256)Kbps ? 2048Kbps = 192Kbps.

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Figure 7: Network model for simulation The average-degrade algorithm reduces the bandwidth levels of the ows i7 , i6 and i8 . After the adaptation, the bandwidth levels of the ows i7 , i6 and i8 are: Flow Bandwidth level i7 128Kbps i6 128Kbps i8 128Kbps The bandwidth levels of all other ows remains unchanged. After the adaptation, avail list = (i10 ; i1 ; i0 ; i3 ; i4 ; i5 ; i2 ; i9 ; i7 ; i6 ; i8 ). However, this order of the ows in the list may change when their average bandwidths are recomputed. Number of ows whose bandwidth changed = 3.

6 Performance Evaluation To evaluate and compare the performances of the above rate adaptation schemes, we ran several simulation experiments. From these experiments we determined the values of the performance parameters time count, hando count, var average bw, var bw var and mean bw change. 6.1 Simulation Model We used a simple network con guration to evaluate and compare the performances and fairness properties of the above three schemes (Figure 7). In this con guration, the network has a star topology. There are ten wireless cells, C1-C10, each covered by a base station. The cells are nonoverlapping and are arranged in a ring con guration. There is a central node N to which each of these base stations are connected by a link of in nite bandwidth. The wireless link at each cell has a bandwidth of C Mbits/sec. A mobile node can move to any of its two neighboring cells on the ring. Each ow originates at the central node and the data

ows downstream to a mobile host in a cell via the base station of that cell. We considered only unicast ows.

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Figure 8: Set I : time count vs. mobility rate

6.2 Parameters Apart from the performance parameters mentioned at the beginning of this section, there are many parameters associated with the ows and host mobility. We have taken measurement data for dierent values of these parameters. These parameters are:  ow arrival rate : The rate at which new ows arrive.  ow duration : Duration of a ow.  ow spec : Data trac speci cation of a ow. A ow can operate at several bandwidth level. Usually, the data trac of a ow operating at a particular bandwidth level is described by a token bucket lter[8] consisting of the token generation rate, bucket depth and the peak rate. In our experiments, we considered only

ows which generates data packets at a constant rate at each bandwidth level of its operation.  cell stay time : The period of time after which a mobile host moves to a neighboring cell.  mobility spec : The length of the ring over which a mobile host may move. This is expressed in the number of adjacent cells of the ring. 6.3 Simulation Experiments We performed several simulation experiments to measure and compare the performance of the dierent rate adaptation schemes by varying the dierent ow and mobility parameters. We have chosen the values of dierent ow and mobility parameters as follows. We assumed poisson arrival of ows i.e. interarrival times between successive ows is exponentially distributed. Flow duration and cell stay time are also exponentially distributed. The size of mobility spec has a uniform distribution within the range [2, 10]. In the following we describe the notations used for ow and mobility parameters:

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 a : Mean ow arrival rate in number of ows per second  df : Mean duration of ows.  m : Mean mobility rate in number of moves per second.

Then, mean cell stay time = 1/mean mobility rate.  s : Mean mobility spec in number of adjacent cells. We performed two types of experiments: homogeneous (Set I) i.e. when the ows have the same data trac characteristics, and heterogeneous (Set II) i.e. when the ows have dierent data trac characteristics. We ran each simulation for 6000 seconds of simulation time and the reported data were taken from the later 4000 seconds.

6.4 Simulation Results In both homogeneous and heterogeneous experiments, we measured the values of the performance parameters by varying the mean mobility rate while keeping all other parameters xed. In all of the experiments, the following parameter values were kept xed:  d = 300 seconds  s=5  a = 3.0 ows/second 6.4.1 Homogeneous In the homogeneous experiments, all ows have the same bandwidth requirements and levels of operation. We conducted several sets of simulation for several dierent ow bandwidth requirements. Here we describe the results of one such experiment in which the capacity of each wireless link C and bandwidth levels l of the ows are as follows: C = 2 Mbps.

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Figure 11: Set I : var bw var vs. mobility rate

l = (128Kbps; 112Kbps; 96Kbps; 80Kbps; 64Kbps). In Figures 8 and 9 we plot the variation of time count and hando count, respectively, with mobility rate. With the increase in mobility rate, hando rate increases. As a result, the bandwidth demand in a cell uctuates more frequently. This causes more frequent rate adaptation and the rates of a higher number of ows change over the entire simulation period. Thus the message overhead per second increases with mobility rate. But, the total number of handos, for which rate adaptation was initiated, also increases. As a result the number of ows whose rates are changed per hando remains almost invariant of the mobility rate. As expected, the message overhead (both time count and hando count) in the fair adaptation scheme is signi cantly higher than the

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Figure 13: Set II : time count vs. mobility rate 6 average-fair fair minimum

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message overhead in both minimum and average-fair adaptation schemes. But the signi cant result is that, the message overhead in average-fair scheme is almost same as the message overhead in the minimum adaptation scheme. In Figures 10-12, we compare the fairness characteristics of the three rate adaptation schemes. From Fig. 10, we see that, in the average-fair adaptation scheme, the variance of the average bandwidth of the ows are much smaller than the corresponding variances in minimum and fair adaptation schemes. This happens due to the following reasons. In minimum adaptation scheme, some ows may operate at higher bandwidth levels compared to some other ows throughout their lifetime. Thus, the average bandwidth obtained by dierent ows at the end of their duration may vary widely. In fair adaptation scheme, the available bandwidth in a cell is fairly distributed to the ows in that cell, but a ow may receive dierent bandwidth at dierent cells and dierent ows may visit dierent set of cells. Thus, the average bandwidth obtained by dierent ows may be different. In average-fair adaptation, the criteria for selecting

ows for upgrading or degrading is that the average bandwidth obtained by the ows in the cell till that point of time are balanced. Thus the variation of the average bandwidths of the ows is less than those in minimum adaptation and fair adaptation. In Fig. 11, we compare the parameter var bw var for the three dierent rate adaptation schemes. A high value of var bw var means that, the variations of rate suered by dierent ows dier widely; whereas a small value of var bw var means all ows suer similar rate variations. In minimum adaptation scheme, some ows suer wide variations in their bandwidth, whereas some ows suer smaller variation due to rate adaptation. In fair adaptation scheme, the available bandwidth is fairly distributed to the ows in a cell. Hence, all ows suer similar rate variation. In Fig. 5, the var bw var values in average fair adaptation scheme lies between those values in minimum and fair adaptation schemes because of its particular ow selection criteria for adaptation. Fig. 12 shows that the mean bw change increases as mo-

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Figure 14: Set II : hando count vs. mobility rate bility rate increases. This is because, with increase in mobility, the number of handos and rate adaptations increases. For a given mobility rate, fair adaptation has the highest mean bw change, minimum adaptation has the lowest and mean bw change of average-fair scheme lies in between fair and minimum adaptation. Thus, from these simulation results we observe that, the average fair adaptation scheme has low network overhead, but has good fairness characteristics as measured by the parameters var average bw, var bw var and mean bw change.

6.4.2 Heterogeneous In the heterogeneous experiments (Set II), we used three dierent classes of ows with bandwidth levels l as follows:

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7 Conclusion and Future Work In this paper we investigated the tradeo between the network overhead and fairness property of rate adaptation schemes in a multimedia network supporting mobile hosts. We characterized the fairness property of rate adaptation in a mobile environment with some measurable parameters. We have described two rate adaptation schemes: fair adaptation, which allocates the available bandwidth in a link fairly to all ows on that link but has high network overhead; and minimum adaptation, which has low network overhead but is unfair in terms of bandwidth allocation to the ows. A new rate adaptation scheme, average-fair adaptation, is presented which has low network overhead but has good fairness properties. We have compared the performances of these three schemes by simulation experiments. Simulation results show that, in both homogeneous and heterogeneous ows, averagefair adaptation scheme has low network overheads, but

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1. l = (128Kbps; 112Kbps; 96Kbps; 80Kbps; 64Kbps). 2. l = (256Kbps; 224Kbps; 192Kbps; 160Kbps; 128Kbps). 3. l = (384Kbps; 352Kbps; 320Kbps; 288Kbps; 256Kbps). C = Capacity of each wireless link = 6 Mbps. The results of these experiments are shown in gures 13-17. In these experiments too, the performance characteristics of the three rate adaptation schemes are similar to those in the homogeneous experiments. The network overheads of the average-fair adaptation scheme are very close to those of the minimum adaptation scheme and are signi cantly less than the overheads in fair adaptation (Figures 13 and 14). In Fig. 15, the var average bw in average-fair adaptation is much less than those in fair and minimum adaptation schemes. The values of the parameters var bw var and mean bw change in average-fair adaptation lie between those values for fair and minimum adaptation (Figures 16 and 17).

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Figure 17: Set II : mean bw change vs. mobility rate its fairness characteristics (as measured by the parameters var average bw and var bw var) are good compared to the fair and minimum adaptation schemes. As part of future work, we need to perform more simulation experiments to study the impact of ow and mobility parameters on the network overhead and the fairness properties of the rate adaptation schemes. Also, we plan to investigate the impact of various tuning parameters on the rate adaptation schemes.

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