Different Algorithms for Normal and Protection Paths

Journal of Network and Systems Management, Vol. 13, No. 1, March 2005 ( C© 2005)DOI: 10.1007/s10922-005-1845-6

Different Algorithms for Normal and Protection Paths

Rajarshi Gupta,1,2 Eric Chi,1 and Jean Walrand1

Many network routing situations commonly require backup paths that satisfy variousconstraints on bandwidth, link or node selection, and ease of configuration. In this paper,we attempt to validate whether it is beneficial to have distinct algorithmic treatmentsof normal and backup path calculation, configuration, and maintenance. We presenta modular suite of algorithms that enable us to manage normal and protection pathsdifferently. In the process, we develop a simple extension of Minimum InterferenceRouting Algorithm for shared protection paths. We incorporate a distributed algorithmto separately calculate normal and backup paths in the network, using link state infor-mation, and present an evaluation of asynchronous dynamic reorganization of backuppaths to reduce congestion in the network. Simulations demonstrate nontrivial quanti-tative reductions in blocking probabilities under certain conditions. We conclude thatin order to choose an optimal algorithm for a protected QoS routing application, it isrecommended to also consider a combination of two different algorithms for normaland backup paths.

KEY WORDS: Optical networks; MPLS; protection paths.

1. INTRODUCTION

Many network routing situations require a protection path in addition to a normalpath. For example, Multiprotocol Label Switching (MPLS) and optical networksrequire backup paths that satisfy various constraints on bandwidth, link, or nodeselection, and ease of configuration. In this work, we examine the premise thatalgorithmic treatments of backup path calculation, configuration, and maintenanceneed not be the same as those applied to the corresponding normal paths.

We present a mechanism by which the network operator may utilize differentalgorithms for normal and protection paths. Our research does not categoricallyadhere to any of the particular algorithms presented here—the very motivation

1Department of Electrical Engineering and Computer Sciences, University of California Berkeley,Berkeley, California.

2To whom correspondence should be addressed at 211 Cory Hall #1772, Berkeley, California 94720-1772. E-mail: [email protected]

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14 Gupta, Chi, and Walrand

for a modular infrastructure, in fact, is to facilitate incremental schemes. Were-use many well-known routing and control protocol techniques. In order toprovide a flexible mechanism, however, we have also developed some novelschemes:

� A distributed method for separately calculating normal and backup pathsin the network, using link state information

� Per-link state maintained at each node, that allows optimal sharing ofbackup bandwidth

We also consider asynchronous dynamic reorganization of backup paths toreduce congestion in the network.

To validate our ideas, we have developed a modular simulation model thatenables us to add or remove specific algorithm components, in addition to vari-ous measurement modules that track performance statistics such as call blockingprobabilities and link loads. The plan is to study the interaction of the variousmechanisms (current as well as future)—which will allow us to choose the opti-mal suite of algorithms for a specific application scenario.

The rest of the paper is organized as follows. In Section 2 we describe twoapplication scenarios for this research. In Section 3, we take a closer look at hownormal and protection paths differ and discuss how to exploit these differences.The algorithms are discussed in Section 4. Sections 5 and 6 present the simulationmodel and a quantitative analysis of improvements gained using these methods.We close with Conclusion and Future Works sections.

2. APPLICATIONS

Differentiating protection path and normal path management has immediaterelevance to two cutting-edge technologies deployed in the internet today.

MPLS [1] is a label-switched scheme widely deployed today to achieve qual-ity and control on a connection carried over IP. Among its many benefits, MPLSprovides an infrastructure that supports fault-redundant paths. The framework(Section 3) described here is directly applicable to an MPLS network, employingan ReSerVation Protocol-like (RSVP) [2] mechanism to reserve and tear-downpaths. The mechanisms described in Section 4.2 can also be considered in anMPLS context.

In optical networks, wavelengths need to be allocated across optical cross-connects before traffic can flow across them. Extremely high bandwidths associ-ated with fibers warrants the presence of a backup path to ensure rapid fail-overs.Finding suitable normal and protection paths is a common and critical problem inoptical networks [3].

Since wavelengths are a limited resource on each link, the control plane mustkeep track of the current allocations and judiciously deal with oncoming demands.

Different Algorithms for Normal and Protection Paths 15

The need is for a dynamic system that handles the routing and configuration ofprotection paths.

The management of normal and backup paths need not be considered inMPLS and optical network contexts separately. In fact, the ideas presented herewill be useful in any other domains that require the configuration of multiplenormal and protection paths through a network.

3. NORMAL VS. PROTECTION PATHS

In this section we describe the motivation behind a key concept in our paper:protection paths and normal paths need not be managed in the same way.

3.1. Different Routing Algorithms

Several sophisticated algorithms for the calculation of paths in a networkhave been developed, and significant effort has also gone into the computationof protection paths (e.g., [3–5]). The metric behind calculating the normal andprotection paths may differ depending on the application.

For example in an optical network when a new wavelength λ needs to berouted through the network, frequently the path that has the greatest minimumnumber of λ available on any link [6] is chosen. When a protection path throughthe same network is determined, a λ is assigned so that the cumulative allocation ofprotection λs is minimally increased (e.g., this scheme is employed in the AT& TIP Backbone Optical Network). Re-using existing provisioned λ ensures that thebackup path minimally consumes additional protection resource in the network.

In this example we see that the optimization objectives are different for anormal and a protection path wavelength assignment. In this paper, we study themerits of this design decision.

3.2. Cost of Reconfiguration

Many of today’s network applications (e.g., bandwidth allocation across thecountry) employ greedy algorithms, because future demand is unknown. And anygreedy algorithm that deals with dynamic demands is liable to leave a networkshouldering an unbalanced load. In today’s world of guaranteed Service LevelAgreements (SLAs), it is imperative that even brief service outages (caused byreconfiguration) be infrequent. Frequent reconfiguration of a live normal path foroptimal redistribution of network load is out of the question.

Protection paths, on the other hand, are not subject to such constraints. Anonlive protection path (i.e., one that is not actively carrying any traffic), maybe reconfigured without affecting the current traffic. Thus, we are encouraged toreconfigure these paths if a more balanced allocation of the network resources canbe achieved.


3.3. Decoupled vs. Coupled Algorithms

The algorithms listed in the references above may broadly be classified intotwo categories—coupled algorithms, which compute the normal and protectionpaths simultaneously, and decoupled algorithms, which first compute the normalpaths and then separately compute the protection paths. Clearly, coupled opti-mization techniques will always perform better than decoupled ones, because thedecision-making process is open to more possible actions to take. The simplicityand flexibility (Sections 3.1 and 3.2) offered by the decoupled schemes, however,can often make them more desirable. For that reason, we deal with only decoupledalgorithms.

4. NEW ALGORITHMS

In this section we present a distributed mechanism by which we can applydifferent treatments to the normal and protection paths.

4.1. Summary of Algorithms

All the schemes described here have the following underlying mechanisms.

� Every source knows:

– Topology of the network– Available bandwidth for every link in the network

� A new request arrives at the source and is characterized by the source anddestination, as well as the normal and protection bandwidths (bN and bB)

� Based on its knowledge of the network, the source runs a source-basedlocalized algorithm to generate the normal path:

– The source makes a request along the normal path– All nodes in the path reserve the requested bandwidth

� The source then repeats the algorithm on a modified graph (without thelinks on the normal path) to generate the backup path

– A request is sent for a protection path. The request also carries the normalpath information in addition to the requested protection bandwidth

– Each node in the backup path reserves a protection bandwidth.� A periodic link-state advertisement scheme conveys the link state infor-

mation to every node in the network� The sources also carry out a periodic reconfiguration of the protection

paths. Specifically, each source wakes up after a random amount of timeand checks to see if any of its protection paths are using links that are ap-proaching capacity. If so, it attempts to reconfigure those protection paths.


4.2. Algorithm Details

In this section, we describe in detail what was summarized above.

4.2.1. Algorithm for Normal PathTo calculate the normal path for the request, we need to employ an algorithm

that is distributed and source-based. The most common such algorithms are short-est path algorithms like Dijkstra [7] and we can utilize these (see Section 5). Wealso consider variations like Minimum Interference Routing [8].

All algorithms, however, should meet certain conditions.

� A link may not reserve traffic beyond its capacity� Shorter paths are preferred because they consume fewer network resources� Critical resources, e.g., residual bandwidth in bottleneck link, should be

set apart for future demands

The last two conditions reflect that what we really seek is to lower the blockingprobability of call requests or equivalently increase the network utilization.

4.2.2. Link Weight MetricA source-based routing algorithm like Dijkstra uses link weights to compute

the best path. The link weights chosen essentially determine the behavior of thealgorithm. The appropriate choice of the link weights and the path objectivefunction depends on the specific network context.

4.2.3. Request-Response for Normal PathThe scheme for reserving the normal path is very similar to the RSVP protocol

[2] used by MPLS. To make a reservation request, the source needs the pathinformation and the normal bandwidth that it is trying to reserve.

At every hop, the node determines if adequate bandwidth is available in theonward link. Else it rejects the requests and sends a response back to the source.If bandwidth is available, it is provisionally reserved, and the request packet isforwarded on to the next hop in the path.

If the request packet successfully reaches the destination, the destinationacknowledges it by sending a reservation packet back along the same path. Aseach node in the path sees the reservation packet, it confirms the provisionalreservation of bandwidth. In addition, it also performs the required configurationneeded to support the coming traffic. This could include setting up labels for anMPLS system, or configuring the λ switching for an optical switching system.

4.2.4. Link Utilization ValuesIn order to accept/reject an incoming request, every node must have knowl-

edge of its reserved bandwidth on each outgoing link. For each outgoing link, the


node needs to keep track of three values:

� BT := The total bandwidth available on this link.� BN := The normal bandwidth reserved on this link. This is the total amount

of traffic that has been reserved on this link for normal paths.� BB := The protection bandwidth on this link. This is the maximum amount

of bandwidth reserved on this link to support protection traffic.

The available bandwidth, BV , on a link is calculated as

BV = BT − BN − BB

When a new request with bandwidth bN is received by the node, capacity limitsrequire that bN ≤ BV for every link in the path. Further, every node on the backuppath needs to provision the resources required to support the backup bandwidth(bB), in case of a failure in the normal path.

Traditional methods of calculating backup paths often do not account for thesharing of bandwidth between various backup paths and consequently utilize thenetwork resources poorly. Much recent research work has gone into the develop-ment of algorithms for this “Shared Protection Path” problem (e.g., [9–11]). In[12], we extend upon these works to leverage correlation of the release of reservednormal bandwidth with the switch over of protection bandwidth during a singlelink failure. Normal bandwidth need no longer be reserved along all the linksif a link on the normal path fails. Consequently, normal bandwidth reservationmay at times be shared with protection bandwidth reservation. We exploit thisfact to more accurately calculate the value of BB and thereby achieve greater net-work utilization. In [12] we derive analytical upper bounds on the improvementin utilization and also present very common network scenarios where significantimprovements will be realized.

4.2.5. Request-Response for Backup PathThe request-response mechanism for the backup path works in the same way

as that of the normal path. The source sends a request along the backup path. Aseach node receives the request, it calculates if it can accept the request. If so, itmakes a provisional reservation. The request for the backup path is different inthat in addition to the path information and the backup bandwidth, the requestalso carries the list of links in the normal path. This is necessary for accuratelyupdating the link states [12].

When the acknowledgement comes back from the destination, the nodes per-form the necessary configurations required to be prepared for oncoming protectiontraffic and update the link states.

4.2.6. Link Weight Metric for Backup PathFor calculating the backup path, we could employ the same algorithm and

metric as used for the normal path (Section 4.2.1), with the links used for the


normal path removed from the network. As discussed throughout this paper we areencouraged to explore other algorithmic options for protection path computation.For instance, the objective could be to minimize the cumulative backup resourcesallocated in the entire network (see Section 3.1).

4.2.7. Link State AdvertisementsFor the calculation of normal and backup paths the sources need to know

the current state of the network. Specifically, every source needs to know theavailable bandwidth for every link in the network. Consequently, the link-stateupdate mechanism for our distributed mechanism needs to exchange the per-linkBV values. Since the amount of per-link state information is very small, anyappropriate link state advertisement scheme like those employed by OSPF [13] orBGP [14] should be adequate for this purpose.

4.3. Asynchronous Reconfiguration of Backup Paths

We employ a scheme to periodically reconfigure the protection paths to reducecongestion in the bottleneck links [15, 16]. Every source carries out the followingmechanism:

� Wakes up after a random interval� Upon waking up, examines its current records of link states to identify

congested bottleneck links (i.e., links whose BV is less than some thresh-old)

� It checks if any backup paths originating from itself use the bottlenecklink

� If so, it tries to calculate an alternate backup path. This may be calculatedby routing a new path on a modified graph without the links on the normalpath, as well as the bottleneck links.

� If a “better” alternative path is found, it reconfigures the backup path.An alternative backup path is said to improve the network congestion ifit improves some pre-decided global metric (e.g., number of congestedlinks)

In Section 6 we present simulation results to demonstrate the benefits ofperiodic reconfiguration of backup paths and the situations when this mechanismought to be used.

5. ANALYZING DIFFERENT NORMAL AND BACKUPROUTING ALGORITHMS

5.1. Algorithms Simulated

To test claims in Section 3.1, we consider applying different routing algo-rithms to normal and protection paths. We used three different algorithms forcalculating the primary path and added a fourth algorithm (Minimum Cumulative


Backup) for the backup paths. We simulated all the twelve pairings on threetopologies.

The four algorithms used are explained below:

5.1.1. Least LoadedAs the name suggests the routing algorithm searches for the route with the

most spare capacity.

5.1.2. Minimum Hop CountThis is the standard Dijkstra’s shortest path algorithm.

5.1.3. Minimum Cumulative BackupThis chooses the path that minimizes the increase in the total amount of

protection resources reserved in the network (see example in Section 3.1).

5.1.4. Minimum Interference Routing Algorithm (MIRA) [8]This is a modification of Dijkstra’s shortest path algorithm. The links that are

critical to source-destination pairs are assigned higher weights. A link is classifiedas critical for a given source-destination pair if routing a flow on it would reduce themaximum flow between the said source-destination pair. Every source-destinationpair has an associated weight, and the weight of a link equals the sum of theweights of all the source-destination pairs for which it is a critical link. Thus,critical links may be made more or less “critical” by particular source-destinationpairs that have greater assigned weights. In our experiments, all source-destinationpairs were assigned a weight of 1. So all pairs were considered equally important.

Some explanation is needed as to how MIRA was extended to protection pathrouting. When a connection request arrives the MIRA extension should choosea path that interferes the least with all the maximum flows between the othersource-destination pairs. Interfering means reducing not just the maximum flowfor primary paths but also a maximum flow for backup paths since connectionsare admitted only if both a primary and backup path are found.

Computing an exact protection maximum flow for other source-destinationpairs by taking into account bandwidth sharing, however, does not make sense.A protection route is a function of the primary path it is protecting. A futureprotection flow can be determined only after the primary path it is protecting hasbeen determined. Computing a maxflow for future protection flow for a source-destination pair requires foreknowing what primary path will be chosen for thatsource-destination pair.

Thus, we compute only one maximum flow for each of the other source-destination pairs when the primary route is being chosen. This is done instead ofcomputing two maximum flows—one for primary flows and another for protection.This is reasonable since both the primary and backup paths will be branches within


the maximum flow anyway, if at least two disjoint paths exist. So critical links inthe single maximum flow for a source-destination pair would indicate potentialinterference to both future primary and protection flows.

When MIRA is used to compute a backup path, an explicit primary path hasalready been chosen—so backup bandwidth sharing can be exploited. Indeed itis possible that using a link for a primary path would reduce the maximum flowbetween another node pair but does not reduce the maximum flow when used for abackup path. In such a case that link is not considered critical. Thus, we maintainthe spirit of MIRA in our extension.

5.2. Scenarios

In each of the following scenarios some subset of all the node pairs actas sources and destinations. Connection requests originate at the source for aconnection request of primary bandwidth of one unit and backup bandwidth ofone unit. The backup path must be link disjoint with the primary path, and thenetwork must be robust to single link failure. Primary and backup path routing isdecoupled. So a primary path is determined first. If a path is found, then a backuppath is determined. If it is found, the connection is admitted into the networkand appropriate primary and backup resources are reserved [12] and held for theduration of the connection. If either primary or backup path is not found the requestis blocked.

In the first two topologies a small subset of the nodes are chosen to besource- destination pairs. In the third topology, almost all node pairs act as source-destination pairs.

5.2.1. MIRA TopologyConsider the network shown in Fig. 1(a) (This is the same topology used to

demonstrate the performance of MIRA [8]). Four pairs of nodes on the “edge”of the network are chosen as source-destination pairs. The thin links can carryup to 6 calls while the fat links can carry up to 24 calls. Thus, the thin and fatlinks represent OC-12 and OC-48 links, respectively. All call arrival processes areMarkovian, i.e. Poisson arrivals with rate λ and exponential holding times withrate µ. The arrival intensity is the same for all four source-destination pairs.

5.2.2. Ring of Rings TopologyThe network shown in Fig. 1(b) represents a typical metropolitan network.

The larger center ring consists of links with capacity 48 and the smaller ringsconsist of links with capacity 12 to represent OC-48 and OC-12 links, respectively.Again there are four source-destination pairs; connection requests arrive as aPoisson process with intensity λ and connections hold for exponential times withrate µ. All source-destination pair statistics are independent and identical.


Fig. 1. Topologies.

5.2.3. USA TopologyThe network shown in Fig. 1(c) is made in the image of the AT&T IP

backbone [17, 18]. The fat links have capacity 24 and the thin ones capacity 6to represent the capacity ratio between OC-192 and OC-48 links. The numbersjust to the outside of the nodes represent a score that is roughly proportionalto the number of optical links with capacity less than OC-48 incident on thenode. The higher the node score the more likely the node is to be a source or adestination for a connection request. The assumption is that a node with a greaterdegree of sub OC-48 links is more likely to generate or terminate a connectionrequest.

Again connection arrivals and holding times are Markovian. This time, how-ever, all node pairs may act as source-destination pairs with intensity proportionalto the sum of their scores (Some sums are zero. No traffic is sent between thesepairs.). So connections arrive for pair [10, 12] at a rate four times as great as therate they arrive for pair [0, 3]. The actual intensity values were chosen so that theblocking rates observed were in a reasonable range—about 2–3%.


5.3. Results

5.3.1. MIRA ToplogyFigures 2(a–c) compare the blocking probabilities under different loads λ/µ

using different algorithm combinations. All blocking probabilities were computedover a single realization. All simulations were run long enough so that the estimatedblocking probability did not vary in the thousands digit if the simulation run timewas increased by a factor of 10.

We can make a few observations from the above graphs. Using the leastloaded algorithm for backup path routing uniformly performs the worst. For bothminimum hop and MIRA algorithm for the normal paths, using the same algorithmfor the backup path does the best, albeit only slightly better than using otheralgorithms for backup path.

Fig. 2. MIRA topology: Total blocking probabilities.


Fig. 3. MIRA topology: Comparing the best combi-nation for different normal path algorithms.

Figure 3 compares the best backup path curves, for each of the normal pathalgorithms. The combination of MIRA primary routing and MIRA backup routingyields the lowest blocking probability in the MIRA topology.

5.3.2. Ring of Rings TopologyTable I shows the total blocking rates observed when the load is λ/µ = 3.

Each column lists the blocking rates observed when using the algorithm at the topof the column for primary paths and the algorithm indicated by the row for backuppaths.

It is not too surprising that the blocking rates are almost all identical becausethere are very few routing options in the topology and different algorithms typicallychoose the same paths. What is interesting is that using MIRA for primary pathrouting yielded a blocking rate that was nearly 29% worse. Apparently MIRA ismore willing to pick longer paths more often than the other algorithms and in ringnetworks is heavily penalized for doing so. This is actually a strength of MIRAin mesh networks where MIRA takes into account a routing decision on the nearterm future to choose the better of two alternative paths that are more or less thesame number of hops.

Table I. MAN Total Blocking Probabilities

Least Loaded Min Hop MIRA

Cumulative Backup 0.06527 0.06527 0.08446Least Loaded 0.09616 0.09616 0.11728Min Hop 0.06527 0.06527 0.08446MIRA 0.06527 0.06527 0.08446


Table II. USA Total Blocking Probabilities

Total Load = 20 Total Load = 24

Least Loaded PrimaryCumulative Backup 0.01863 0.03238Least Loaded 0.03357 0.05330Minimum Hop 0.01841 0.03756MIRA 0.01338 0.02526

Minimum Hop PrimaryCumulative Backup 0.02363 0.03997Least Loaded 0.03173 0.05035Minimum Hop 0.02264 0.03756MIRA 0.01791 0.03196

MIRA PrimaryCumulative Backup 0.02082 0.03525Least Loaded 0.02999 0.04842Minimum Hop 0.02526 0.03271MIRA 0.01490 0.02728

5.3.3. USA TopologyTable II shows the total blocking rates observed under different loads. Each of

the three possible primary path algorithms is given a subtable. The algorithms listedper row of subtable indicate the corresponding backup path routing algorithm. Theblocking rates were obtained for two different load scenarios. The first columnholds blocking rates when the total load between all source-destination pairs was20; the second column holds values when this load was 24.

Interestingly using the least loaded algorithm for primary path routing andMIRA for the backup path yields the lowest blocking rate among all the combi-nations. In particular this blocking rate was approximately 10% less than whenusing MIRA for both the normal and backup paths and 50% less than when usingleast loaded for both paths. In general using least loaded routing for the backuppath yielded results that were significantly worse than all the other combinations.

Recall, however, that the arrival rates are different for different node pairs, butall critical links regardless of node pair are assigned the same weight. Thus, MIRAfor primary path routing is likely not performing as well because it is choosinglonger paths in order to avoid links important to even node pairs, which generatelittle traffic.

6. OCCASIONAL RECONFIGURATION OF BACKUP PATHS

We now turn our attention to reconfiguring backup paths, to get a sense ofthe possible gains in performance as we tune the rate at which the reconfigurationis carried out.


Routes assigned to incoming path demands should be assigned so that theblocking probability is minimized in some sense. Admitting a connection acrossa given route incurs the opportunity cost of future connection requests beingblocked. Intuitively we expect that a connection request should be routed in a waythat balances the load across the network to best match the demand offered to thenetwork.

6.1. Rebalancing Backup Paths for a Single Source

Each (s, d) pair has an alarm clock that rings periodically. To avoid synchro-nization problems clock rings are randomized. When a (s, d) pair’s clock rings,the backup paths for that (s, d) pair are re-routed to better balance network load,if a better routing allocation exists.

We focus on the following example for illustrative purposes. Bandwidth iscounted in units of connections and each link can support up to C connections.We consider gains achieved for a single source-destination pair (s1, d1) when itperiodically rebalances its backup paths. Assume (s1, d1) uses only one route forprimary paths and uses n routes that are link disjoint with each other and withrespect to the primary route, for backup paths. We assume disjoint protection pathsin order to determine an upper bound on the gains. Protection paths are assignedindependently per connection.

For all (s, d) pairs in the network, connection requests arrive as a Poissonprocess with rate λsd . Each connection holds for an exponentially distributedamount of time with holding rate µ independent of the arrival processes and otherholding times. The alarm clock rings of (s1, d1) occur as a Poisson process with rateγ . The blocking probability is nonincreasing with the number of available backuppaths n. To make computations tractable, we assume that on every link in eachbackup path the aggregate cross-traffic connections arrive as independent Poissonarrivals with an intensity scaled by the complement to the aggregate blockingprobability.

A control decision is made when one of two events occurs. When a connectionrequest arrives and there exists sufficient capacity to support the primary path andat least one backup path, the algorithm chooses one of the backup paths. When(s1, d1)’s alarm clock rings, (s1, d1) chooses some re-distribution of the backuppaths over all the possible backup routes. A reward of one unit is earned for everyadmitted connection.

Equivalently we may associate a penalty of one unit for every blocked connec-tion request. Minimizing the penalty function or maximizing the reward functioncorresponds to minimizing the overall blocking probability into the network.

Thus, we have the makings of a Markov Decision Process (MDP). Figure 4provides a picture of our MDP problem where n = 3. Only the links comprisingthe three backup paths are shown. Links 0–4, 5–9, and 10 to 11 comprise threebackup paths. The primary path is not shown.


Fig. 4. Full model.

Note that the blocking probability will likely be dominated by certain bot-tleneck links. For example in Fig. 4, we may have that λ2 > λi for i = 0, 1, 3, 4,λ9 > λj for j = 5, 6, 7, 8, and λ11 > λk for k = 10, 12. Thus, we assume for agiven load profile on the network that all the blocking will occur on the mostheavily loaded link in each of the backup paths. Figure 5(a) provides a picture ofthe approximated control problem that (s1, d1) is faced with for n = 3, λa = λ2,λb = λ9, and λc = λ11.

We compute the blocking probability as a function of load for the scenariodepicted in Fig. 5(a). We bound blocking probabilities in the worst case wherebackup paths cannot share bandwidth reservations on any links—all λi calls arebackup paths for other (s, d) pairs with no overlap with (s1, d1) primary path.Under this worst case, (s1, d1) backup paths cannot share bandwidth on any links.

We took C = 10 and λ := λs1d1 = λa = λb = λc. Arriving calls are routedto the least loaded link. Upon clock rings, switchable calls are routed to the leastloaded link. Ties are broken by choosing at random among the links with themaximum spare capacity.

We computed blocking probabilities for λ/µ such that the blocking proba-bilities were on the order of 1 to 2% for γ = 0, 10,∞ and µ−l = 1. The totalblocking probability as a function of load λ/µ is shown in Fig. 5(b).

We notice that if up to 1% blocking probability is tolerated, it is possibleto achieve a 10% gain in network load (λ/µ ranges from 4 to 4.5) if γ is takento be sufficiently large. Note also that for a load of λ/µ = 4.5 a 1% blockingprobability can be achieved if γ = ∞ whereas the blocking probability is 2% ifno rebalancing is allowed.

Figure 6(b) shows the blocking probability for the switchable paths as a func-tion of load. Blocking probabilities for the fixed connections are shown in Fig. 6(a).Note that as γ increases the blocking probability for the switchable connectionsactually increases. What is happening is that by intelligent rebalancing of the


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network load switchable calls are arriving to a better balanced and consequentlymore loaded network.

6.2. Rebalancing Backup Paths for Two Sources

Consider a slightly more elaborate topology and demand load shown inFig. 7(a). We now have two links of interest that carry both primary and backuppaths and two sources that generate with equal likelihood primary and backuprequests. The backup paths for the two sources have primary paths not shown thatare link disjoint and thus may share bandwidth. C is again taken to be 10 and wevary the arrival intensity λ at both sources. Calls are routed to the least loadedlink. Uniform randomization breaks ties. Here we allow primary paths to also bererouted. Thus gains with increasing load should only be more pronounced. Theresulting blocking probabilities for the backup paths are shown in Fig. 7(b).

There is only a marginal improvement by varying the rate at which the pathsare rerouted. Although not shown, gains in blocking probability for the primarypaths are no less marginal. Having two sources that are routed into the networkinitially under a load balancing rule tends to keep the network overall balancedmore often than not. So postadmission rerouting corrections have very little benefit.In the previous numerical example, much larger gains are achieved because poorgreedy decisions occur more frequently.

All network topologies and traffic matrices will be mixtures of the two basicconfigurations and load profiles. The subsequent performance gains will be some“convex combination” of the performance gains of the first case and the second.

7. CONCLUSIONS AND FUTURE WORK

We considered the hypothesis that gains could be leveraged out of distinctlytreating normal and protection paths, and discussed advantages of such schemes.


We then presented techniques to glue together different normal and protection al-gorithms in a distributed fashion. In the process, we developed a simple extensionof Minimum Interference Routing Algorithm for shared protection paths. To ana-lyze our premise, we computed the blocking probabilities on different topologiesusing different combinations of routing algorithms for primary and backup pathcalculation. Our routing experiments indicate that depending on the topology anddemand matrix the lowest blocking rates may be achieved by using different al-gorithms for primary and backup paths. The occasional reconfiguration of backuppaths also reduced the blocking rates, though the gains were less significant as thenumber of source-destination pairs increased.

It is well known that given a topology and some idea of future demands,there are multiple algorithms to determine the normal and backup paths. Of these,one may be better suited than the others for the current situation. We want topoint out that it may be possible to use a different algorithm for the normal vs.the backup path, with a manageable amount of overhead. In fact, under somesituations, the mixed algorithm might perform the best. The lesson to be learnedfrom this work is that in order to choose an optimal algorithm for a protectedQoS routing application, it is recommended to also consider a combination of twodifferent algorithms for normal and backup paths.

We are continuing to run simulations for different scenarios to better un-derstand why certain algorithm combinations do better than others under specificscenarios. It may be that the best combination is sensitive to the traffic matrix.Moreover, if the objective is not the blocking rate but some other metric at a dataplane level (e.g., latency), it is not clear how different combinations would fare.Poisson traffic and blocking performance is more appropriate in an MPLS settingbut not as helpful in evaluating performance in optical networks. While there issome churn in the demands in an optical network, the trend is for connections toarrive and persist indefinitely. Assuming this traffic load model, a better metric tofollow would be network capacity utilization.

Both of these issues are directions that warrant more exploration. Eventuallywe want to extend this work to a framework whereby a given network topology andpredicted demand scenario will allow us to determine the best possible combinationof normal and backup path routing.

ACKNOWLEDGMENTS

We acknowledge the most valuable contributions of Dr. John Strand—hisideas, suggestions, and comments were extremely helpful. We also acknowledgethe contributions of Tian Yu, for his help in coding the simulator used in this work.

REFERENCES

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Rajarshi Gupta is a PhD candidate in Electrical Engineering and Computer Sciences at theUniversity of California at Berkeley and will graduate in May 2005. Prior to this, he completed his MSdegree in 1999 at Berkeley and his BS degree in 1997 from the University of Maryland. From 1999 to2003, Rajarshi worked with Extreme Networks as a Senior Designer, where he has been the author of8 patents. He is interested in algorithms to ensure quality in networks—both wired and ad-hoc. Thisincludes: analysis of network capacity; switching and scheduling mechanisms for efficient utilizationof resources; and, routing algorithms to guarantee quality of service.

Eric Chi received his MS degree in Electrical Engineering and Computer Sciences from theUniversity of California at Berkeley in 2001 and his BA degree in physics in 1999 from Rice University.His work focused on distributed network capacity management. He has worked on inventory restockingproblems and protection path resource allocation in wired communication networks.


Jean Walrand received the PhD degree from the Department of Electrical Engineering andComputer Sciences of the University of California at Berkeley where he is now Professor. His researchinterests include decision theory, stochastic processes, and communication networks. He is the authorof An Introduction to Queueing Networks (Prentice Hall, 1988) and of Communication Networks:A First Course (2nd ed. McGraw-Hill, 1998) and coauthor of High-Performance CommunicationNetworks (2nd ed, Morgan Kaufman, 2000). He is a Fellow of the Belgian American EducationFoundation and of the IEEE and a recipient of the Lanchester Prize and of the Stephen O. Rice Prize.

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Different Algorithms for Normal and Protection Paths