A Comparison of Hard-state and Soft-state Signaling Protocols

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1 University of Massahusetts Amherst Amherst Computer Siene Department Faulty Publiation Series Computer Siene 2003 A Comparison of Hard-state and Soft-state Signaling Protools Ping Ji University of Massahusetts - Amherst Follow this and additional works at: Part of the Computer Sienes Commons Reommended Citation Ji, Ping, "A Comparison of Hard-state and Soft-state Signaling Protools" (2003). Computer Siene Department Faulty Publiation Series. 99. Retrieved from This Artile is brought to you for free and open aess by the Computer Siene at SholarWorks@UMass Amherst. It has been aepted for inlusion in Computer Siene Department Faulty Publiation Series by an authorized administrator of SholarWorks@UMass Amherst. For more information, please ontat sholarworks@library.umass.edu.

2 A Comparison of Hard-state and Soft-state Signaling Protools Ping Ji, Zihui Ge, Jim Kurose, and Don Towsley Computer Siene Department, University of Massahusetts at Amherst, Abstrat One of the key infrastruture omponents in all teleommuniation networks, ranging from the telephone network, to VC-oriented data networks, to the Internet, is its signaling system. Two broad approahes towards signaling an be identified: so-alled hard-state and soft-state approahes. Despite the fundamental importane of signaling, our understanding of these approahes - their pros and ons and the irumstanes in whih they might best be employed - is mostly anedotal (and oasionally religious). In this paper, we ompare and ontrast a variety of signaling approahes ranging from a pure soft state, to soft-state approahes augmented with expliit state removal and/or reliable signaling, to a pure hard state approah. We develop an analyti model that allows us to quantify state inonsisteny in single- and multiple-hop signaling senarios, and the ost (both in terms of signaling overhead, and appliation-speifi osts resulting from state inonsisteny) assoiated with a given signaling approah and its parameters (e.g., state refresh and removal timers). Among the lass of soft-state approahes, we find that a soft-state approah oupled with expliit removal substantially improves the degree of state onsisteny while introduing little additional signaling message overhead. The addition of reliable expliit setup/update/removal allows the soft-state approah to ahieve omparable (and sometimes better) onsisteny than that of the hard-state approah. I. INTRODUCTION One of the key infrastruture omponents in all teleommuniation networks, ranging from the telephone network, to VC-oriented data networks, to the Internet, is its signaling system. Two broad lasses of signaling approahes an be identified: so-alled hard-state and soft-state approahes. Between these two extremes lie signaling approahes that in pratie borrow various mehanisms from eah. Despite the fundamental importane of signaling, our understanding of these two approahes - their pros and ons and the irumstanes in whih they might best be employed is still not well understood. Broadly speaking, we assoiate the term soft-state with signaling approahes in whih installed state times out (and is removed) unless periodially refreshed by the reeipt of a signaling message (typially from the entity that initially installed the state) indiating that the state should ontinue to remain installed. Sine unrefreshed state will eventually timeout, soft-state signaling requires neither expliit state removal nor a proedure to remove orphaned state should the state-installer rash. Similarly, sine state installation and refresh messages will be followed by subsequent

3 2 periodi refresh messages, reliable signaling is not required. The term soft-state was oined by Clark [3], who desribed the notion of periodi state refresh messages being sent by an end system, and suggested that with suh refresh messages, state ould be lost in a rash and then automatially restored by subsequent refresh messages - all transparently to the end system, and without invoking any expliit rash-reovery proedures:... the state information would not be ritial in maintaining the desired type of servie assoiated with the flow. Instead, that type of servie would be enfored by the end points, whih would periodially send messages to ensure that the proper type of servie was being assoiated with the flow. In this way, the state information assoiated with the flow ould be lost in a rash without permanent disruption of the servie features being used. I all this onept soft state, and it may very well permit us to ahieve our primary goals of survivability and flexibility... Roughly speaking, then, the essene of a soft-state approah is the use of best-effort periodi state-installation/refresh by the state-installer and state-removal-by-timeout at the state-holder. Soft-state approahes have been taken in numerous protools, inluding RSVP [9], SRM [9], PIM [6], [5], [7], SIP[0] and IGMP[4]. Hard-state signaling takes the onverse approah to soft state - installed state remains installed unless expliitly removed by the reeipt of a state-teardown message from the state-installer. Sine state remains installed unless expliitly removed, hard-state signaling requires a mehanism to remove orphaned state that remains after the state-installer has rashed or departed without removing state. Similarly, sine state installation and removal are performed only one (and without state refresh or state timeout), it is important for the state-installer to know when state has been installed or removed. Reliable (rather than best-effort) signaling protools are thus typially assoiated with hard-state protools. Roughly speaking, then, the essene of a hard-state approah is the reliable and expliit installation and removal of state information. Hard-state approahes have been taken in protools suh as ST-II[3], [7] and Q.293b[4]. Between the extremes of a pure hard-state approah and a pure soft-state approah lie many protools that have adopted elements of eah approah. Indeed, protools that were initially oneived as pure soft-state protools have adopted a number of hard-state mehanisms (often as extensions) over time. For example, in IGMPv[4], soft-state timeout at a router was used to detet the departure of previously registered hosts; IGMPv2/v3 [8], [2] later added an expliit leave message to allow a host to expliitly inform the state-holding router of its departure. In the original RSVP [9], PATH and RESV state installation messages were transmitted best-effort under the assumption that the loss of a signaling message would be reovered from via a later refresh message; ACK-based reliable signaling was introdued as an extension to RSVP in [] and was also suggested in [2]. RSVP has also provided for expliit (although optional) removal of filter speifiations sine its oneption. Hard-state protools have adopted elements of the soft-state approah as well. In the ST-II hard-state signaling protool, periodi HELLO messages serve to inform the HELLO sender that all is well with its neighbors, and that its own state that relies on a given neighbor is still valid - an impliit refreshing of its state. Given the blurred distintions between hard-state and soft-state approahes and the fat that protools that fall into one ategory will adopt mehanisms typially assoiated with the other, we believe that the ruial issue is not whether a hard-state or a soft-state approah is better in some absolute sense. Instead, we believe that the more fundamental question is to understand how the mehanisms that have evolved into being inluded in various hard-state and soft-state signaling protools an best be used in given situations, and why. The goal of this paper is to answer

4 3 this question. In this paper, we thus ompare and ontrast a variety of signaling approahes ranging from a pure soft-state approah, to soft-state approahes augmented with expliit remote state removal and/or reliable signaling, to a pure hard-state approah. We define a set of generi protools that lie along this spetrum, and develop a unified parameterized analyti model that allows us to quantify a key performane metri assoiated with a given signaling protool - the fration of time that the state of the state-installer and the state-holder are inonsistent [5]. We also quantify the ost (both in terms of signaling overhead, and appliation-speifi osts resulting from state inonsisteny) assoiated with a given signaling approah and its parameter values (e.g., state refresh and removal timeout intervals). Among the lass of soft-state approahes, we find that a soft-state approah oupled with expliit removal substantially improves state onsisteny, while introduing little additional signaling message overhead. The addition of reliable expliit setup/update/removal further allows the soft-state approah to ahieve omparable (and sometimes better) onsisteny than that of the hard-state approah. Our work fouses on evaluating the performane of different signaling protools. However, there are other nonperformane-oriented omplexity of various signaling approahes (e.g., the omplexity of protool implementation), whih may be examined by other evaluation mehanisms, and is beyond the sope of this paper. The remainder of this paper is strutured as follows. In setion II, we desribe five different signaling protools that inorporate various hard-state and soft-state mehanisms, and qualitatively disuss the fators that will influene performane. Setion III-A presents an analyti model for examining the performane of these approahes in the single-hop ase, and ompares their performane. Setion III-B onsiders the multi-hop ase. Setion IV disusses related work. Finally, setion V summarizes this paper and disusses future work. II. SOFT-STATE, HARD-STATE AND PROTOCOLS IN BETWEEN Fig.. Signaling sender and reeiver: messages and mehanisms In this setion, we desribe the operation of five different abstrat signaling protools. These protools differ in the manner in whih state is installed, maintained, and removed, and whether seleted signaling messages are transported best-effort or reliably. We will onsider a single node (that we will refer to as the signaling sender ) that wishes

5 4 to install, maintain, and eventually remove (or have removed) state at a remote node (that we will refer to as the signaling reeiver ). We onsider the simple, but illustrative, example of a signaling sender having a loal state value that it wishes to install at the signaling reeiver. When the signaling sender state value equals the signaling reeiver s installed state value, we will say that the values are onsistent [5]; otherwise the sender and reeiver state values are inonsistent. Our goal here is not to model a speifi signaling protool suh as RSVP or Q293b, but rather to apture the essential aspets of identifiably different approahes towards signaling. After desribing the protools, we then onsider the performane metris by whih these protools an be evaluated, and qualitatively disuss the fators that will impat performane. We will onsider the following five approahes: Pure soft-state (): In this approah, the signaling sender sends a trigger message [] that ontains state installation or update information to the signaling reeiver, and starts a state refresh timer (with value ). When the state-refresh timer expires, the signaling sender sends out a refresh message [9] ontaining the most up-to-date signaling state information, and resets the refresh timer. Trigger and refresh message are sent in a best-effort (unreliable) manner. When a trigger or refresh message is reeived at the signaling reeiver, the orresponding signaling state information is reorded and a state-timeout timer (with value ) assoiated with this state is started (or restarted if it was already running). Signaling state at the signaling reeiver is removed only when its state-timeout timer expires; that is, state will be maintained as long as the reeiver ontinues to reeive refresh messages before the state-timeout timer expires. This timeout ould our beause the signaling sender is no longer sending refresh messages (beause its loal state has been removed and it thus wants the remote state to be removed at the signaling reeiver), or beause refresh messages have been lost in transmission, and have resulted in a state timeout at the signaling reeiver. We will refer to the latter ase as false removal of state, sine the signaling sender did not intend for this state to be removed. Soft-state with Expliit Removal (+ER) signaling: +ER is similar to the approah, with the addition of an expliit state-removal message. When state is removed at the signaling sender, the sender sends a best effort (unreliable) signaling message to the signaling reeiver arrying expliit state-removal information. State refresh and trigger messages, and state-timeout timer are all employed as in the ase of. Soft-State with Reliable Trigger messages (): is similar to with two important additions. First, trigger messages are transmitted reliably in. Eah time a trigger message is transmitted, the sender starts a retransmission timer (with value ). On reeiving an expliit trigger message, the destination not only updates signaling state, but also sends an aknowledgment to the sender. If no trigger aknowledgment is reeived before the retransmission timer expires, the signaling sender resends the trigger message. Seondly, also employs a notifiation mehanism in whih the signaling destination informs the signaling sender about state removals due to state-timeout timer expiration. This allows the signaling sender to reover from false removal by sending a new trigger message. Soft-State with Reliable Trigger/Removal message (R) : R is similar to the approah, exept that the R approah uses reliable messages to handle not only state setup/update but also state removal. Hard-State () approah: In the approah, reliable expliit messages are used to setup, update and remove state at the signaling reeiver. Neither refresh messages nor soft-state timeout removal mehanisms are employed. A ruial onern with any hard-state protool is the removal of orphaned state at the signaling reeiver. Beause the hard-state protool laks the timeout of state removal, it must rely on an external signal to detet that it is holding

6 5 orphaned state. This signal an be generated for example, by a separate heartbeat protool whose job is to detet when the signaling sender rashes and then inform the signaling reeiver of this event. Alternatively, the external signal might be generated via a notifiation from a lower layer protool at the signaling reeiver that had an assoiation with a lower layer protool at the signaling sender and hene an detet signaling sender rashes. One suh an external notifiation (signal) is reeived, the hard-state signaling approah leans up the orphaned signaling state assoiated with the signaling sender. One ompliating fator is that of false notifiation - the external signal may falsely detet a signaling sender rash (this would our, for example, if a series of heartbeat messages were lost, but the signaling sender was still operational). As in the ase of, false notifiation an be repaired by having the signaling reeiver notify the signaling sender (if it exists) that its orphaned state has been removed. A signaling sender whose state has been inorretly removed an then send a new trigger message. Figure illustrates the messages and mehanisms used by the signaling sender and reeiver in the various signaling protools. In the following setion, we will develop a unified parameterized analyti model that allows us to quantify a key metri assoiated with a given signaling protool - the fration of time that the state of the state-installer and the stateholder are onsistent (i.e., have the same value). Clearly, we would like this value to be as lose to as possible. In addition to quantifying onsisteny, we would also like to quantify the ost assoiated with a given signaling approah and the level of onsisteny it is able to ahieve. One aspet of this ost will be the signaling message rate itself. A seond aspet of this ost is the ost assoiated with being in an inonsistent state. For example, in IGMP, when an end host leaves without signaling its departure to its edge router, multiast data will ontinue to flow towards the reeiver (even though the reeiving host is no longer in the multiast group) - a ost. In the ase of a hierarhial peer-to-peer file-sharing system in whih a lient uploads the names of the files it shares to a server when it joins the P2P network, but then leaves the network without signaling its departure, the inonsistent state at the server will result in other peers attempting to ontat the departed peer - again, a ost. In setion 3, the ost funtion we adopt is a weighted sum of the signaling overhead and appliation-speifi osts (suh as unwanted multiast data flows, or onnetion attempts to a departed peer in the examples above). Before delving into the details of the performane models, let us onlude this setion with a qualitative disussion of the fators that will influene performane: Appliation-speifi inonsisteny ost. As noted above, these are the osts assoiated with the signaling sender and reeiver being in inonsistent states. Clearly, when this ost is high, the signaling sender may want to inur a higher signaling overhead in order to keep the signaling sender and reeiver states as onsistent as possible. Refresh timeout value. As noted in [], the smaller the value of the refresh timer, the sooner that onsistent state will be installed at the state-holder, and onsequently the smaller the appliation-speifi ost due to state inonsisteny. However, this advantage omes at the ost of an inreased signaling rate. If the appliation-speifi ost of inonsistent state is high, however, this inreased signaling ost may be warranted. Soft-state timeout value. Sine this timer is meant to remove state that is not refreshed, we would ideally like this value to be as small as possible in order to remove orphaned state as soon as the signaling sender departs. However, too small a timeout value an result in false state removal. Signaling message loss. As the probability of message loss beomes higher, we expet that the fration of time that the signaling sender and reeiver states are inonsistent will also inrease, as it will take longer for either a

7 6 message to be delivered reliably, or for a best-effort refresh message to be delivered. In ases of high loss and high appliation-speifi inonsisteny osts, we expet those protools with expliit reliable transfer to be preferable. Number of hops. In ertain signaling protools suh as RSVP and AFSP[8], a signaling sender must install state at multiple nodes between itself and the ultimate signaling destination. As the number of hops inreases, the fration of time that all nodes are in an inonsistent state will also likely inrease. In the following setions, we will develop an analyti model that will allow us to quantitatively explore these issues and intuition. III. MODELING AND ANALYSIS OF SIGNALING APPROACHES We begin our analysis by onsidering the simple example of a single node (the signaling sender ) that an install, maintain, hange, and eventually remove (or have removed) a single piee of state information at a remote node (the signaling reeiver ). We fous here on a single piee (rather than multiple piees) of state, as it is oneptually simpler and the latter an generally be onsidered as multiple instantiations of the former. The installation, maintenane, hange, and removal of state is aomplished using one of the five abstrat signaling approahes desribed in the previous setion. We assume that the signaling sender and reeiver ommuniate over a network that an delay and lose, but not reorder, messages. A. Signaling in a Single-hop System We first onsider a single-hop system, in whih the signaling sender and reeiver are the only two entities involved in the signaling protool. As shown in Figure 2, we an think of the two entities as being onneted through a single S D S D (a) single physial hop (b) multiple physial hops with end-to-end signaling Fig. 2. single-hop signaling systems logial hop, whih may onsist of one or more physial hops. A number of existing appliations and protools fit this simple single-hop model. For example, signaling in the IGMP protool [4] ours between an end system and its first-hop router. When the end system joins a multiast group, state indiating this group membership must be installed in the first-hop router; when the end host leaves the multiast group, this state should be removed from the router. In ertain peer-to-peer file sharing appliations suh as Kazaa [], a peer registers its shared files with a server (a supernode in the ase of Kazaa), whih then redirets peers seeking a given file to peer nodes that have that file. A peer s registration of its files at a supernode is a single-hop signaling proess, where the signaling sender is the peer, the signaling reeiver is the supernode, and the signaling state ontains the identities of the shared files and the fat the peer is in the system and serving files. ) Model Desription: Before desribing our system model, we first briefly disuss the events that an our during the life yle of a signaling sender/reeiver pair. Signaling state setup. When the signaling session first installs (initializes) its loal state, it transmits a signaling message ontaining the state to the reeiver. After some delay, the signaling message reahes the remote reeiver, enabling both sender and reeiver to ahieve onsistent state.

8 7 Signaling state update. A sender may also update its loal state. As in the ase of state setup, the sender then installs the new state value at the reeiver. When a sender updates its loal state, the sender s and reeiver s state will be inonsistent until the update suessfully propagates to the reeiver. Signaling state removal. At the end of the lifeyle, the sender will remove its state. At this point, the reeiver s state should also be removed. One the sender has removed its state, the reeiver s state is stale (inonsistent) until it is removed. A number of protool-dependent mehanisms (inluding state-timeout, and expliit removal messages) an be used to remove reeiver state. False signaling state removal. The destination may inorretly remove state, even though the sender is still maintaining state. This an our as a result of various protool-dependent events. For example, in soft-state approahes, the state-timeout timer ould expire at the reeiver and remove state, even though the sender is still maintaining state. 465 E>F 798 :9;! #"$% &'#()+*-,./#0+2!3 This state does not exist in model for or.?6@ = A6B <>= C>D State setup State update State removal False removal Fig. 3. A ontinuous time Markov model for signaling approahes in single-hop system Given these events in the lifeyle of a signaling sender and reeiver, we an develop a Markov model, shown in Figure 3, to apture this behavior. The Markov model s states are defined as follows. Eah state onsists of a pair of values, GIHKJ6L-HNM>OPL where HKJ and HNM refer to the states of the signaling sender and reeiver, respetively: Markov state GRQKL$STO aptures the initial stage of the lifeyle, when signaling state has been installed at the sender but not at the reeiver. This is an inonsistent state, sine the sender and reeiver s state values do not math. Markov states G!SULVQWO orrespond to ases where the sender has removed the state, but the reeiver has not. These states are also inonsistent. When the sender and reeiver have onsistent signaling state, the state of the Markov hain is X. When the sender and the destination have different signaling state (i.e., both have installed state, but the state values are different), the Markov hain is in states X Y. When the signaling state is removed from both the sender and the reeiver, the system enters an absorbing state represented by Markov state G!SULSTO. Note that eah of the inonsistent states, GRQNLSTO, GVSUL!QWO, and XY are further divided into two separate Markov states distinguished by subsripts and 2, the purpose of whih is to apture protool-dependent details that we will desribe shortly. In Figure 3, a shaded arrow indiates the initial state of the Markov hain, and the double irled state GVSUL$STO

9 Y Z Z Z 8 is the absorbing Markov state. The transitions among the Markov states are illustrated in Figure 3 with different line styles indiating the different events (state setup, state update, state removal and false removal) that ause state transitions. The system parameters onsidered in the state transitions are: Z+[ : signaling state update rate M : \6] M is the sender s mean signaling state lifetime ZN^ : false state removal rate at reeiver : signaling hannel delay `+a : signaling hannel loss rate In addition, we have the following previously-disussed protool speifi parameters: : soft-state refresh timer value : soft-state state timeout timer value. : message retransmission timer value for reliable transmission We model the signaling state lifetime and the interval between signaling state updates as exponentially distributed random variables (with means \>] M and \>] Z [ Z ^, respetively), false removal as a Poisson proess with rate, and message losses as independent Bernoulli trials with parameter ` a. Furthermore, we approximate the soft-state refresh interval, state-timeout interval, message-retransmission interval and hannel delay as exponentially distributed random variables with means,, and L respetively. In Setion 2, we disussed five different approahes towards signaling. Eah of these approahes an be modeled using the model shown in Figure 3, with different transition rates (and in some ases disabled transitions) for eah of the approahes. We next desribe the model transitions for eah of these different signaling approahes. These transitions are shown either in the model diagram or in Table. Soft-State () model. The initial state of the model, GbQNLSTOP, orresponds to the reation of new signaling state at the sender. As disussed earlier, this results in a trigger message being sent to install state at the reeiver. After a hannel delay, one of two events an our. First, the trigger message an suessfully reah the destination. This event ours with probability G!\S ` a O, and is modeled by the transition from state GbQNLSTO to state X with rate G!\S ` a O-] The seond possibility is that the trigger message is lost. This event ours with probability ` a, and is represented by the transition from GbQNLSTO- to GRQNLSTO!d with rate Ǹa ]. Eventually a refresh message will reah the destination. Sine refreshes are sent periodially with interval, and eah message reahes the destination with probability (\es `a ), there is a transition from GRQKL$STOVd to state X with rate G!\fS Ǹa O]6. The update proess is similar to the setup proess. When the state is onsistent, i.e., the Markov hain is in state X, a state update auses the Markov hain to transit from = to state Xg Y Z [ at rate. The trigger message suessfully arrives at the reeiver with probability (\hs `Ka ) and average delay, whih orresponds to a transition bak to X at rate GV\US ` a O-]. While in XY, the loss of the trigger message auses the Markov hain to transit to state XY d at rate ` a ] a. With rate GV\TS ` a O-]6, the Markov hain transits from state XY d bak to state X. Note that an update may also our when the system is in state GbQNL$STO d or state XY d, whih auses the Markov hain to transit to state GRQKL$STO or state X Z [ respetively with rate. Our model serializes events in the signaling proess. For example, it does not allow a state update while a trigger message is on its way to the reeiver. We assume that an update happens either before a previous trigger message is sent out or after the trigger message has already reahed the reeiver (or has been lost)..

10 o a Z Z Sender signaling state is removed at rate M, i.e., a sender has a session of mean length \6] M9i If the signaling state is removed at the sender before the reeiver has obtained the state, the Markov hain simply transits from GbQNLSTOjd to the absorption state G!SULSTO. However, if the reeiver has already installed state information either onsistently or inonsistently, i.e., the system in state Xd Y or state X, the Markov hain transits to state GVSUL!QWOj. Thereafter, the reeiver must wait for the state-timeout timer to expire in order to remove the orphaned state. We model this by letting the Markov hain transit from state GVSUL!QkO to state G!SULSTO with rate \6]>. Note that the Markov model for does not inlude the GVSUL!QkO d state in Fig. 3. Finally, state an be removed at the destination due to the lak of refresh messages before the state-timeout timer expires. This is modeled by a Markov hain transition from states X, Xld Y, to state GRQKL$STOVd Z ^ with rate i Sine suh false removal only happens when all refresh messages within a state timeout timer duration have been lost, we approximate the probability of this event as ǹmporq-skt a Z ^ Z ^. Therefore, an be expressed as X ùmporq-snt. Note that, the model does not allow a state transition from Xl Y to GRQNLSTO6L due to the serialization onsiderations noted above. Soft-State with Expliit Removal (+ER) model: Reall that in +ER, a signaling message arries expliit state removal information (in addition to the state-timeout mehanism) to remove signaling state. We model this expliit removal by modifying the state removal proess in the model as follows. When the Markov hain enters state G!SUL!QkO as a result of sender state removal, an expliit state removal message is sent out. With probability (\vs ` a ) and after a hannel delay, this message arrives at the destination and triggers the removal of the orresponding state. We model this by letting the Markov hain transit from G!SULVQWOj to the absorbing state GVSUL$STO with rate G!\US Ǹa O-] The loss of the expliit removal message auses the Markov hain to transit from G!SUL!QkOw to G!SUL!QkO!d. From there, the system transits to the absorbing state G!SULSTO at rate \>]6, apturing the state removal aused by the state-timeout timer expiration. Soft-State with Reliable Trigger messages () model: The Markov model for differs from the model for in that, when a trigger message arrying state setup/update information is lost, either a suessful refresh message or a suessful retransmission of the trigger message an bring the Markov hain from state Y X d or state GbQNLSTO d to state X with rate GV\6]> yxz\6]9 O {}G!\fS ` a O. Soft-State with Reliable Trigger/Removal message (R) model: The Markov model for R differs from the model for in that, when an expliit removal message is lost, the system waits for the state-timeout timer to expire or a suessful retransmission of the removal message to go into state G!SULSTO. Thus the transition rate from state GVSUL!QWOVd to state GVSUL$STO is \>]6 ~xzgv\fs Ǹa O-]>. Hard-State () model: The model is similar to the R model, exept that the transition rates assoiated with refresh messages and state-timeout timers are exluded. In addition, as disussed in Setion II, the approah must rely on an external signal to reover from sender failure. Aounting for the related ost of suh an external signal is diffiult, sine it depends on the underlying sheme that performs the failure-detetion for the hard-state approah. For instane, a link-layer sensing mehanism provides failure detetion to signaling without introduing extra signals; whereas failure-detetion relying on an underlying heart-beat exhanging mehanism may have an overall overhead omparable to that of R. Nonetheless, we onsider the failure-detetion as a separate omponent in the system arhiteture with the signaling mehanism. Therefore, in our paper, we exlude this part from the analysis. However, we assume that the external signal an be falsely generated with rate Z, whih auses a faulty removal of a signaling state in the approah.. 9

11 Z Œ Ž Z Z 0 We summarize the protool-speifi state transition of the Markov hain for different signaling approahes in Table, where ZN ƒ denotes the state transition rate from Markov state to. Transition rates Zr +ER R Œ ˆ and Z p ˆŠ K Œ-ˆŠ p ˆŠ K Ž Z p ˆŠ K Œ ˆ Z and Z p ˆŠ K Žwˆ Zr and Z ˆ P Œ ˆŠ ˆ P Ž Z eˆ j IŒ-ˆŠ eˆš K Z eˆ j Ž ˆŠ eˆš K Z ^ Ž `+a ] Ǹa ] Ǹa ] `+a ] Ǹa ] Œjˆ G!\fS ` a O] G!\ S ` a O-] G!\fS ` a O-] G!\fS ` a O-] G!\ S ` a O-] Ž ˆ GV\fS Ǹa O]6 G!\fS `+a O-]6 GV\6]6 xz\6]> UO { GV\fS Ǹa O GV\6]> yxz\6]9 ho { G!\fS `+a O GV\fS Ǹa O]9 S ` a ] S ` a ] ` a ] \6]> G!\fS `+a O] \>]6 G!\fS `+a O-] G!\ S `+a O-] S \>]6 S \6]6 ~x G!\fS ` a O]9 GV\fS ` a O]9 ùmporq-snt a ]> ǹmpo q-skt a ]6 ǹmpo q-skt a ]6 ùmporqskt a ]> ZN TABLE I MODEL TRANSITIONS 2) Model Solution and Performane Calulations: Using this model, we an now study the performane of the signaling approahes disussed in Setion II. We are interested in the following metris: the inonsisteny ratio,, defined as the fration of time that the signaling sender and reeiver do not have onsistent state values; and the normalized average signaling message rate, š, defined as š œx M6, where is the total number of signaling messages required during the lifetime of a signaling session (i.e., time from when the signaling state is initiated until it is removed from the system), and \6] M is the expeted lifetime of the sender s signaling session. Sine the lifetime of the signaling session at the reeiver varies with the signaling approah while \>] M is invariant, the normalization provides a fair omparison between different signaling approahes. To obtain the inonsisteny ratio,, we need to know the fration of time that the system spends outside state GžXUOPL before it eventually transits to the absorbing state G!SULSTO. This is equivalent to evaluating the sum of the stationary probabilities of the inonsistent states in the reurrent Markov model where the absorption state G!SULSTO and the starting state GRQKL$STO- are merged. Let Ÿ following expression for : X Ÿ be the stationary probability of the reurrent Markov model in state. We have the p ˆŠ K IŒ x Ÿ $ˆŠ Ž x Ÿ x Ÿ x Ÿ eˆ j IŒ x Ÿ ˆ P Ž X \ S Ÿ () To obtain the total signaling message overhead,, we need to ompute the average lifetime of a signaling state,, and the mean signaling message rate š : Here, X {š (2) is derived from alulating the mean time to absorption for state GRQKL$STO in the transient Markov model, and š is obtained by onsidering in whih state and with what rate eah of signaling messages - expliit trigger and removal messages, soft-state refresh messages, retransmission and aknowledgment messages - are generated during the signaling proess. We proeed as follows.

12 Z Ÿ Ÿ Ÿ Ž Ž Ž Ž With a suessfully transmitted trigger message, the Markov hain transits from state GRQKL$STOw or X Y to state X, and if a trigger message is lost, the Markov hain transits from state GRQNLSTOj to GbQNLSTO!d or from X Y to Xhd Y. Thus the mean message rate for expliit triggers, šw, is, š} X p ˆŠ K IŒjZ p ˆŠ K Œ-ˆ xyÿ p ˆŠ K IŒjZ p ˆŠ K Œ-ˆŠ p ˆŠ K Ž xyÿ Œ Zr Œ ˆ x Œ Zr Œ ˆ (3) Similarly, the mean message rate for expliit removal, šk Vª, is š!ª XzŸ ˆ j Œ Z eˆ j Œ ˆŠ eˆš x Ÿ ˆ j Œ Z eˆ j Œ ˆŠ eˆ j Ž (4) Soft-state refresh messages are generated at mean rate \6]> when the Markov hain is in states GRQKL$STO d, X, or XY d. Therefore the mean message rate for refresh messages, š ª, an be expressed as, š ª X \ { G Ÿ p ˆŠ K Ž x Ÿ x Ÿ O (5) If trigger messages are transmitted reliably, retransmissions will be generated at rate \6]9 when the hain is in states GRQNLSTO d and XY d, and aknowledgment messages will be generated for every transition to state X. Therefore, the mean message rate for reliable triggers, š ª, an be omputed by, š ª X \ G Ÿ p ˆŠ Ž xyÿ Ox «Ÿ Z ˆ x ZK^ G Ÿ x Ÿ O (6) The third term of š}ª is aused by false removal, sine a reliable trigger sheme requires the signaling destination to send a message to the signaling sender notifying it of the removal. Similarly, for reliable removal, the mean message rate š}ª-ª is: š ª-ªTX \ eˆ j Ž x Ÿ ˆ P ŒjZ eˆ j IŒjˆŠ eˆš x Ÿ ˆ P Ž$Z eˆ j ŽwˆŠ eˆš In summary, the overall mean message rate for different signaling protools are as follows: +ER R šœx š xyš ª š Xzš} xyš}ªnxyš}!ª š Xzš} xyš}ªnxyš}ª š Xzš} xyš}ªnxyš}!ª x š}ªv xyš}ªª šœx š} xyš}ªv xyš}ª-ªnxyš}!ª 3) Model Evaluation: We now ompare and ontrast the performane of the five different signaling approahes using our modeling framework. In order to use representative parameter values, let us onsider as an example, the signaling proess between a Kazaa regular peer (hereafter, simply referred to as a peer) and its supernode (as desribed in the beginning of Setion III-A). Unless otherwise noted, we use the following default parameters: ` a X²± i ± ³, X² ±9µ, \>] ZN[ X ³9±, \>] M¹Xº\$» ±¼±, ²X¾½¼, X ¼, ºXÁÀ Z, and X¾± i ±¼± ±k\. These parameter values are hosen to apture the behavior of a Kazaa session: a signaling state is added when the peer starts the Kazaa appliation, and is updated when the peer hanges its olletion of shared files (e.g., a new file is downloaded into its shared diretory). When the peer exits the Kazaa appliation, the peer-state maintained by the supernode should (7)

13 Z Z 2 be deleted. If this state is not removed at the supernode, an inonsistent state will our. As a result, the supernode may respond to other peers inorretly (e.g., direting them to an already departed peer; these other peers may then fruitlessly ontat the departed peer, dereasing the usability of the appliation). 0.7 Inonsisteny ratio 0. +ER R +ER R Average signaling message rate R +ER +ER R Mean lifetime of a signaling state at (a) ÂÄÃ Å Æ signaling sender (seonds): Mean lifetime of a signaling state at (b) signaling sender (seonds): ÇpÈbÉ Ê Fig. 4. Comparison against the time that a singling state exists at the sender (i.e., session length), ËwÌÍWÎ Impat of session length (\>] M ). We first study the performane of different signaling approahes as a funtion of the expeted amount of time that signaling state is installed at the signaling sender, GV\6] M O. In our Kazaa example, this orresponds to a peer s average session length. In Figure 4 (a), we plot the inonsisteny ratio, and in Figure 4 (b), we plot the normalized average signaling message rate š for the different signaling approahes. Figure 4 provides a number of insights into the single-hop signaling system: When the expeted session length inreases, both the inonsisteny ratio and the average signaling message rate derease for all signaling approahes. In the ontext of our Kazaa example, this implies that if Kazaa is used mostly by peers who tend to turn themselves off shortly after starting, as opposed to remaining on for long periods, (e.g., peers use Kazaa for 5 minutes every hour versus 2 hours every day), the system is likely to inur more signaling overhead, with supernodes responding to queries based on stale information. Comparing +ER to, we note that the improvement of +ER over (using the inonsisteny ratio as the performane metri) beomes more signifiant as the average session length dereases. Even when the average session length is on the order of thousands of seonds, the benefit of adding expliit removal is still non-negligible. This is due to the fat that removing orphaned state requires a relatively long wait for the timeout timer to expire, in the absene of expliit removal. More importantly, onsidering the average message rate in Figure 4, we find that when the average session length is on the order of thousands of seonds, the addition of expliit removal introdues negligible signaling message overhead ompared to the approah. While the ost of inluding this apability is so low, our model indiates that it is very useful to inlude expliit removal in soft-state signaling in suh irumstanes. This is beause that the penalty of not using expliit removal is so high. Figure 4(a) indiates that the performane gain (in terms of a redued inonsisteny ratio) ahieved by introduing reliable triggers beomes signifiant when the peers average session length is long. This is evidened by the fat that when the average session length is long, the five approahes are differentiated aording to whether or not they provide reliable triggers. Conversely, when the average session length is shorter (towards the left of Figure 4(a))

14 Õ Ö 3 the five approahes are grouped on the basis of how state removal is performed: those without expliit removal (, ), those with expliit removal (+ER) and those with reliable removal (R, ). We note that for long sessions, when the differenes in trigger message reliability is most pronouned, the inonsisteny ratio is relatively low for all approahes. Also, as shown in Fig. 4(b), the limited benefit of over omes with non-trivial additional signaling overhead. Thus, for these appliation parameters, providing reliable trigger messages does not appear to be very ruial. R provides essentially the same inonsisteny ratio as. This suggests that beyond expliit removal and reliable transmission, any enhanements to soft-state refresh mehanism an provide only modest gains (if any) in the inonsisteny ratio. Indeed, in some ases R already performs slightly better than. Inonsisteny ratio ER R +ER Signaling hannel loss rate: ϞР(a) R Inonsisteny ratio ER R Ñ +ER R R Signaling hannel delay (in seonds): (b) Fig. 5. Comparison against link loss rateò}ó and link delay Ô Impat of message loss and delay. 00 Inonsisteny ratio 0. +ER R x +ER Average signaling message rate 0 +ER R x R x R x 0. x +ER x Soft-state refresh timer (in seonds): (a) Soft-state refresh timer (in seonds): (b) Fig. 6. Comparison against soft-state refresh timer ( ), single hop ase Figure 5 plots the inonsisteny ratio for different signaling approahes for various loss rates (a) and delays (b). Figure 5(a) indiates that even for modest loss rates (e.g., 5%), reliable transmission signifiantly improves the performane of soft-state protools. Figure 5(b) plots the inonsisteny ratio versus the one-way sender-to-reeiver delay. We observe an approximately linear inrease in the inonsisteny ratio under all signaling approahes. However, signaling approahes with reliable transmission exhibit a slightly larger slope. This is beause the value of the retransmission

15 4 timer is generally proportional to the hannel delay. Thus, to reover from loss, approahes with reliable transmission suffers longer latenies in an environment with longer transmission delays, while soft-state approahes that only rely on a refresh mehanism do not. Impat of timer onfiguration. There are three different timers used in the five signaling approahes we onsider: the soft-state refresh timer, the soft-state state-timeout timer and the retransmission timer. Figure 6 explores the performane of different soft-state signaling approahes under different soft-state refresh timer settings. Sine does not employ a refresh mehanism, it is shown as a Ø on the y-axis. When the refresh timer value hanges, we set the state-timeout timer to be 3 times the value of the refresh timer. Figure 6 reveals an interesting tradeoff between having a short refresh timer (to redue the inonsisteny ratio) and a long refresh timer (to keep signaling message overhead low). 00 Integrated ost (C) 0 +ER R +ER Ù R x Soft-state refresh timer value (in seonds): 00 x Fig. 7. Soft-state refresh timer ( ) Overall Cost. As disussed earlier, there are two omponents of overall ost: signaling message ost, and appliation-speifi osts arising from inonsistent state in the sender and reeiver. For example, we saw earlier that for IGMP, this latter ost was the transmission of unwanted multiast data; in the ase of Kazaa, this latter ost was the additional overhead aused by the supernode providing peers with pointers to already departed peers. To evaluate the ost of both signaling overhead and appliation-speifi osts resulting from state inonsisteny, we define an integrated ost (Ú ) as ÚÛXzÜÝ{$ xyš (8) where Ü indiates the relative weight of appliation-speifi ost due to inonsistent signaling state. In Kazaa, for example, Ü might be interpreted as the number of signaling messages assoiated with fruitless queries that are aused by inonsistent file-sharing state at the supernode. In the following, we set Ü to be 0 (msg/se). In Figure 7, we plot the integrated ost assoiated with different signaling approahes versus the soft-state refresh timer value, ( ). From this figure, we observe that there exists relatively sensitive optimal operating points for and, above whih the inonsisteny ost inreases substantially and below whih the message signaling ost inreases signifiantly. Suh an optimal operating point also exists for +ER, although the integrated ost is not very sensitive to rather longer refresh timer values. Last, for R, a longer timer value is preferred, and when the timer is large enough (on the order of 00s of seonds), it provides omparable performane to the hard-state approah.

16 Þ ß 5 Inonsisteny ratio 0. +ER R x +ER Inonsisteny ratio ER R +ER R R x State timeout timer (in seonds): (a) x Retransmission timer (in seonds): (b) Fig. 8. state timeout timer (à ) for soft-state based approahes and retransmission timer á for reliable transmissions Figure 8 (a) explores the impat of different state timeout timer values on the inonsisteny ratio of soft-state approahes. Here we fix the state refresh timer to be 5 seonds and vary the state-timeout timer. The results indiate that, when the state-timeout timer is shorter than the refresh timer, all soft-state based approahes perform poorly, sine refresh messages arrive too late to keep alive the signaling state at the signaling reeiver. One the state-timeout timer value is greater than the refresh timer value, the different approahes behave very differently: R does well with long timeout values, sine the longer the timeout timer, the less likely it is that a state is falsely removed due to loss of refresh messages. and +ER do best when the state-timeout timer is approximately twie the length of the refresh timer, so that the probability of false removal is redued. However, sine longer timeout timers add larger delays to remove orphaned state, and +ER also require the state timeout timer to be short enough to avoid suh problems. Reall that employs a notifiation mehanism in whih the signaling reeiver informs the signaling sender about state removals and the signaling sender reovers from a false removal by sending another trigger message. Sine is the most sensitive to the proess of removing orphaned state and its notifiation mehanism redues the penalty of false removal, it works best with a timeout timer value that is just slightly larger than that of the state-refresh timer. Figure 8 (b) explores the impat of different retransmission timer values on the inonsisteny ratio of the five signaling approahes. Sine depends only on expliit reliable transmissions for state setup/update/removal, it is the most sensitive to hanges in the retransmission timer i Tradeoff between inonsisteny ratio and average signaling message rate. By varying the soft-state refresh timer, we study the tradeoff between the inonsisteny ratio and the average signaling message rate of different signaling approahes, and show the results in Figure 9. Sine hard-state does not use the refresh timer, neither the inonsisteny ratio nor the average signaling message rate vary with ; in Figure 9, hard-state is shown as a single point Ø. Figure 9 also indiates that the onsisteny quality of R is not sensitive to soft-state refresh rate (whih is determined by the refresh timer), whereas the onsisteny qualities of the other soft-state approahes hange with the signaling overhead. We also examined the tradeoffs between inonsisteny ratio and signaling overhead based on other system or design parameters. Figure 0 shows the tradeoff between the inonsisteny ratio and the message overhead by varying the signaling state update rate Z [ (Figure 0 (a)) and by varying the signaling hannel delay (Figure 0 (b)). From Figure 0 (a), we observe that for large inonsisteny probability (â ± i ±+\ ), to ahieve the same onsisteny

17 6 quality, uses the least amount of signaling messages omparing to all other signaling approahes; On the other hand, to ahieve small inonsisteny probability (ãz± i ± ±9À ), should be used to save the signaling overhead. From Figure 0 (b), we observe that the tradeoff urves are not sensitive to hanging signaling hannel delays ER R Message Overhead R 0. +ER Inonsisteny probability Fig. 9. Tradeoff between inonsisteny ratio and average signaling message rate, derived by varying Message Overhead ER R R +ER Message Overhead 0. +ER R R +ER (a) Inonsisteny probability e Inonsisteny probability Fig. 0. Tradeoff between inonsisteny ratio and average signaling message rate: (a) derived by varying ËjÌÍ+ä, (b) derived by varying Ô. While our model assumes exponentially distributed timer values, in pratie, signaling protools usually use deterministi timers. To investigate the impat of our exponential assumption on the timer values, we build simulations that use deterministi timers under the same system settings. Our simulation results indiate that using deterministi timers does not affet our observations and onlusions. For example, in omparison to the evaluation results shown in Figure 4, the inonsisteny ratio slightly differs (ãå\6æ ) between the analytial and the simulation results with deterministi timers. For average signaling message rate, the differene between the analytial and the simulation results is between ½ æ to \6½ æ, while the qualitative relative behavior for different signaling protools remains unhanged. Figure depits the results, where the simulation results are shown as dotted urves with 95% onfidene interval. Simulation results, in omparison to the evaluation results shown in Figure 6, are shown in Figure 2, where we also observe small performane differene (less than 3%) between the shemes of using deterministi timers and using exponential timers.