Dynamic Value-Based Lightpath Allocation in DWDM Networks
, P.Kirkby T.Michalareas, L.Sacks  University College London, Electrical and Electronics Engineering Department,  Nortel Networks, Harlow Labs Abstract— In this paper we propose an algorithm for dynamically allocating end-to-end lightpaths in a WDM network, that can be used in a number of applications (IP over fiber dynamic bandwidth brokers and optical bandwidth exchanges). The optimization target is to maximize the perceived value of the traffic traversing it. We investigate the impact of elastic and inelastic demands on the problem as well as the discrete nature of the WDM circuits and the scarcity of the resource allocated. We compare our algorithm with the alternative of virtual segmentation of the pool of wavelengths between different type of demands and we show the benefits in a series of simulations. Keywords : WDM, Optical bandwidth exchanges, light-path allocation, dynamin bandwidth provision, proportional fairness, multi-bidding algorithms.

I. I NTRODUCTION In the past few years, there has been a tremendous number of advances in optical networking, mainly in the form of wavelength division multiplexing (WDM) that enables multiplication of the available bandwith over the same optical fibre infrastructure. This technology offers point-to-point link adjacencies between nodes in the optical domain. End-to-end services (referred to as light-paths) are offered by wavelength routing algorithms that decide which path should be followed between the source and the destination points and which wavelengths will be used in the intermediate links. The intermediate nodes can act as wavelength converters enabling wavelength switching (fixed, limited or full), although the number of such converting nodes and the number of wavelength conversions is a minimization target for the routing algorithms. The light-paths that are offered by wavelength routing are said to form a virtual topology (as opposed to the physical topology of the optical fibre). In this virtual topology a set of traffic demands is presented and a subset of them that can be satisfied will actually be contracted (leased). This allocation procedure is termed as Light Path (LP) allocation (see [1] for details) and it is analogous to that of Virtual Path (VP) allocation in ATM networks. The end-to-end service appears as a leased line to its subscriber. The allocation algorithm has to decide which subset of the presented set of demands will be satisfied. The simplest allocation algorithm is First Come First Served (FCFS). FCFS does not take into account any special requirements of the demands. It just allocates to them as many lightpaths as they require if they are available. Other more complicated allocation algorithms take into account the individual requiremts of every demand to decide which should be

satisfied (according to an optimization target). The use of WDM technology increases the available capacity the optical carriers have in their disposal. Such increase in the side of the supply can lead to new applications emerging at the optical layer or layers above out of the commoditization of optical connectivity (see [7] , [8], [9] for more details on the commoditization process and architectures to support it). Examples of such applications are : UnContracted Allocation Service : subscribers can ask for additional allocation to their contracted one. The demands do not have a number of required wavelengths but they can have a priority assigned associated with them (elastic demands). The allocation holds for a minimum time interval (at the scale of minutes) that is much shorter that that of normal contracted services (at the scale of months). Optical Bandwidth Exchanges : subscribers can request (and contract) dynamically sets of wavelength aggregates between certain end points. Their demands usually have a number of required wavelengths (inelastic demands). The exchanges act as an e-market place and a switching centre (see [7] , [8] for more details). IP dynamic bandwidth provisioning : subscribers are dynamically allocated bandwidth according to a measure of their time-varying IP traffic load and a set of policies defined by their contract. The demands put on such a system can be both elastic and inelastic. For such applications the wavelength routing and the lightpath allocation algorithms are the critical components of the system, as they are responsible for the optimization of use of the network. In this paper we consider the routing information for a given topology as an input and we focus on the properties of the light-path allocation algorithm. There is also a need for a network management system that will handle interlayer optimization for applications like IP dynamic provisioning that extend more than a single layer (for a proposed management architecture see [2]).



 

II. P ROBLEM

DEFINITION

We assume that the following information is available about the problem : a set of resources that is the physical topology of the network, (fiber connectivity) which is represented as a connectivity matrix C. The capacity of the link is measured in wavelengths, so it has an integer value.



B. Optimization Criteria

1200

Price Willing To Pay for that quantity

inelastic WTP elastic WTP

1000

800

600

400

200

0 0

2

4 6 8 10 12 Demanded Bandwidth (in number of Wavelengths)

14

16

Fig. 1. Examples of elastic and inelastic Willingness To Pay functions of lightpaths x



a set of demands S. Every demand s is characterized by its source-destination pair, a WTP map (as described in the following paragraphs ) that defines its behaviour. a routing table R that defines explicit paths for every considered source-destination pair.



A. WTP maps There are two types of demands considered, elastic and inelastic (in order to cover all uncontracted and contracted applications over the same mutli-service carrier network). Both express their relative value for the end-user in terms of a network currency unit. This end-user’s perceived value for the allocation is termed Willingness To Pay (WTP). The first type is elastic demands that follow a uni-elastic demand function, . expressed in terms of a constant WTP map This type of demands does not require any specific number of lightpaths. It can utilize any number of lightpaths and it can even tolerate the loss of connectivity. The second type is that of inelastic demands. It follows an inelastic demand function (expressed as a step-like WTP map). Every such demand has two parameters associated with it :

 





maxWTP : a maximum amount of network currency they are prepared to exchange for any allocation above their . : the maximum number of wavelength these demands are interested in.



See Figure-1 for an example of both types of WTP maps. The inelastic type models the leased-line contract, currently available in the telecommunications business. Such a contract is used to provide telcos customers with bandwidth capacity according to their long-term predicted needs. The elastic type models a new contract where non-utilized wavelengths are offered to customers for a restricted time (a single period) and then these are renegotiated. Such traffic contracts can be utilized by WDM routers that can dynamically require bandwidth to cope with increased temporal usage of their resources by users.

The optimization criteria for an allocation algorithm depend on the application and the policy of the optical carrier. Although it could be argued that in today’s free market place the ultimate optimization target is revenue, the strategy a carrier follows should be flexible. In our version of the problem we differentiate between the set of metrics and targets to be optimized as set by the operator and the ones that the allocation algorithm uses internally to operate. In this case, on top of the definition of the algorithm, we have to define a set of ”engineering” rules that would map these external optimization targets to internal ones. An example of such a mapping is given in the simulation scenario section. Our algorithm uses internally the idea of proportional fairness. The use of proportional fairness for network optimization, has the advantage that it enables fully distributed and highly scalable solutions. It converges rapidly to deliver the greater value of traffic across the network in any multi-service carrier scenario (see [4]). In this system we use an arbitrary network currency to set both congestion (shadow) prices and to define the value map of any particular service demand. In future, such systems could be linked to real currency (e.g. for real-time bandwidth brokerage). Proportional fairness has also been proposed as a method for allocating rates to TCP sessions in IP networks (see [5]). The formal definition of a vector of allocations is in Equation-1, where is any other vector of feasible allocations and is the vector that holds the values of the demands (for more details see [3]). The rate allocated to a demand is proportional to its value and inverse proportional to the price of resources along the path (that depends on how much demand there is for those resources in total).



 



! %'&(

)+ *  ,  "$#  /- .

(1)

The significant differencies in light-path allocation for WDM networks is that the resources (light-paths) are of discrete nature (number of wavelengths) and they are scarce (for current systems typically 32 wavelengths can be carried at the same fibre). For those reasons the algorithms devised for TCP allocation need to be extended to take into account these two factors. There is another significant difference in our version of the problem from that of packet networks. Usually the assumption is that the WTP map of the demands in packet networks follows an elastic form. In our case we consider inelastic demands (as described in the paragraphs above). The bounded requirements of the inelastic demands imposes another set of constraints on the set of feasible allocations of Equation-1. In order to cope with these extensions of the problem we propose a new multibid allocation algorithm, Dynamic Light-Path Multi-Bid Allocation Algorithm.



The Dynamic Light-Path Multi-Bid Allocation algorithm (referred to as DLMA for the rest of the paper) has to accommodate for the inelastic nature of some of the demands and the discrete nature of the wavelengths. It uses as a function any real-value proportional fair allocation algorithm for elastic demands. In our case we use an iterative algorithm as defined in [6]. The main idea of the algorithm is to compute the total demand in network currency units for resources in every node and then allocate every demand a weighted share of that resource. We will consider such a function fair allocation() as a given for the rest of the paper. A. DLMA Algorithm The algorithm comprises two basic functions. The function that is invoked first, is responsible for producing a real-valued allocation. The second function takes that allocation and produces an integral version of it. The basic time unit that the algorithm is based upon, is the epoch. Users that want to change their utility function or parameter values cannot do so during an epoch. The semantics of an epoch is double. The time interval between epochs defines a basic unit for reservation of resources for a specific allocation. The duration of an epoch defines the available time that the algorithm has to decide on an allocation. A.1 Support for Inelastic Users The main idea is to use the function fair allocation() in a scheme that readjusts demands’ bids in a series of negotiation rounds. The demands have different bidding behaviours according to their type. Elastic demands always bid their maxWTP. Inelastic demands start by bidding a fixed percentage of their maxWTP parameter. In every subsequent round they use their allocation of lightpaths as a signal to re-adjust their bid in an effort to get closer to their value of lightpaths. The inelastic demands have two set of behaviours for re-adjusting their bid. During epochs that the demand tries to get an allocation, its bid has two restrictions. In no step it is allowed to exceed its maxWTP parameter value. In every step it cannot change its bid more than that of a fixed percentage of its maxWTP. During epochs that the demand already has an allocation that has been reserved from a previous epoch its bids are unrestricted. This is not necessary if the network keeps track of the reservation time (in epochs) of the allocation and does not consider for that time the associated resources.





0121435



0121635

A.1.a Use of as a signal. The operation we use to readjust an inelastic demand’s bid is similar to linear extrapolation using two points. The technique is illustrated in Figure-2.

0171435

The demand receives a real-valued allocation of allocation of lightpaths, termed for a specific bid. This is the

1500 User’s bid

III. DYNAMIC L IGHT-PATH M ULTI -B ID A LLOCATION A LGORITHM

1000 maxWTP

500 20% maxWTP bid

0

0

5

xallot

10

number of lighpaths

xreq

Fig. 2. Inelastic User’s Bid Readjustment Behaviour

89 0:121435 ; 8 ;

first point used ,bid . The second point used, is the axes’ origin 0,0 . That implies something about the allocation scheme’s behaviour. If the demand puts a 0 bid in the produce fair allocation() function, the allocated number of lightpaths is expected to be 0. The demand computes the slope of the line that fits between these two points and extrapolates the value of the bid that would give the user the allocation. For this extrapolation to work with a single trial the response of the allocation algorithm should be linear and the rest of the competitors should retain their bids unchanged. The first assumption is not true in real networks, but it can be restated to take account the bounded nature of the capacities of the bottleneck links. The restated assumption then would be that the response of the network allocation scheme is expected to be step-linear, with a linear phase while the values are within the bottleneck link capacity. The second assumption does not hold either as all the nonsatisfied inelastic demands re-adjust their bids; demands can be rejected due to the lack of capacity which changes radically the demand for certain resources. To cope with such situations we have introduced multiple negotiation rounds (iterations). That means that the extrapolation is given more that one chance to estimate the required bid for the required capacity. Initially and while demands are still to be rejected due to the lack of resources the extrapolation process over-estimates the increase of the demand’s bid to achieve an allocation of the required number of lightpaths. We restrict this error by introducing a fixed restriction limit of change. The limit is expressed in terms of a demand’s maxWTP percentage.



0171435

A.2 Producing Discrete Allocations The multiround bidding algorithm produces a real-valued allocation for every accepted demand, trying to maximize the total utility offered by the network to the demands. This realvalued allocation is not feasible for an optical transport layer where the capacities of the links are offered in a granularity of one wavelength. This discrete nature of the resources necessitates the use of a transformation in order to map the real-valued

1.1e+06 DLMA VS_60 VS_25 VS_10

1.4e+06

Total Value of Allocation (in Network units)

Total Value of Allocation (in Network units)

1.6e+06

1.2e+06

1e+06

800000

600000

400000

200000

DLMA VS_60 VS_25 VS_10

1e+06

900000

800000

700000

600000

500000

400000

300000 0

5 10 15 20 25 Number of demands per source-destination pair (mixed)

30

0

5 10 15 20 25 Number of demands per source-destination pair (mixed)

Inelastic-Elastic Users Proportion 60-40%

Fig. 3. Total Value Forwarded for all considered algorithms

30

Inelastic-Elastic Users Proportion 25-75%

Fig. 4. Total Value Forwarded for all considered algorithms

IV. S IMULATION S CENARIO allocations to integer ones. In this algorithm we use the integer part of the real-valued allocation as the initial integer allocation. After this initial step we can calculate how much spare capacity is left in terms of wavelengths to the network’s links. The question we are faced with after this initial allocation is which of the accepted demands will get allocated one extra lightpath or not. Our criteria should distort the maximization of the ”social” utility in the least possible way (the distortion is unavoidable due to the granularity of one wavelength in the capacities of our resources). The second step solves this problem by using the decimal part of the real-valued allocation. The algorithm sorts the demands based on the decimal part of this allocation. It then tries to allocate the extra lightpath starting from the one with the highest decimal part. That effort could fail if the neccesary extra wavelength is not available in every link that comprises the correspondent lightpath. Whenever this extra allocation is feasible the algorithm checks whether any of the links used, has reached its maximum capacity. If such a link is found then the algorithm substracts the demands that need it from the set of demands to be tried for additional allocation. The step is necessary to improve the algorithm’s performance. The algorithm terminates when all the demands have been tried. The criteria we use for sorting is the decimal part of the real-valued allocation. The result of the sorting algorithm can give more than a single demand at the same rank. We call this event a tie. At such an event the algorithm has to decide which of the two or more demands at the same rank should be tried first for allocating an extra wavelength. A number of different policies are possible. One of them is selecting the demand that has the highest value of where x is the current allocation of lightpaths for the considered set of demands and y is the currrent bid of the demand. The rational behind this selection is that we are interested in maximazing the total utility the demands get out of the allocation.

<=?>?@ >A=?B)

BC DE'

In our simulation scenario we considered a case where an operator wants to deal with 4 types of traffic. High priority non-preemptable traffic (inelastic), medium-priority nonpreemptable traffic (inelastic), medium-priority preemptable traffic and low-priority preemtable traffic. The defined proportion of weight that defines the relative priority of the traffic is 1,4,4,16 with higher values indicating higher priority. In order to map those types of users to our algorithm parameters we interpret as priority per wavelength. The parameter then, for inelastic demands (non-preemtable) is the product of the required number of wavelengths and its assigned priority. We scale all WTP by a factor of 1000 to avoid numerical problems. We have conducted a number of experiments altering the proportion of inelastic/elastic users between 60/40 % and 10/90%. The distribution of demands is spatially uniform in a general graph topology with 5 nodes. From the preemptable demands 20% are of high-priority and from the non-preemptable demands 80% are of medium-priority. The for non-preemptable is uniform between distribution of 1 and 2 wavelengths, and the reservation time (in epochs) follows the Poisson distribution with . For every scenario we conducted a number of experiments increasing the number of demands per source-destination pair and selecting the types of the demands according to the defined proportion out of their population. The duration of the experiments is 50 epochs. We measure the sum of the products of the allocated number of wavelengths for a demand by its as an indication of the utility-value of the traffic carried by the network -termed also as pseudo-revenue. The DLMA is compared with 3 versions of a virtual segmentation algorithm. The virtual segmentation algorithm represents a pre-planned solution where a fixed proportion from the pool resources has been dedicated to serve demands only of one type. Inside their segment demands are allocated in a FCFS way. The first variant termed FCFS 60 40 reserves 60% of resources for serving inelastic demands. The second variant termed FCFS 25 75 reserves 25% of resources for serving inelastic demands. The third vari-

F+

F

9I'J

KILJ

MNPO

QGH= 

%GH  

R EFERENCES

Total Value of Allocation (in Network units)

900000 DLMA VS_60 VS_25 VS_10

800000

[1] Mukherjee , B., ”Optical Communication Networks”, McGraw-Hill, 1997. [2] Kirkby, P., ”Management and control of next generation unified carried networks”, UK Teletraffic Symposium, Harlow, May 2000. [3] Kelly, F., ”Charging and rate control for elastic traffic”, European Transactions on Telecommunications, v8,n2, 1997. [4] Kirkby, P., Kadengal, R., Midwinter,J., Biddicombe, M., Carroll, J., Sabesan, S., ”The use of economic and control theory analogies in the design of policy based Dynamic Resource Controlled (DRC) network arUK Teletraffic Congress, Edinburgh, June 1999. chitectures”, [5] Oechslin,P.,Crowcroft, J., ”Weighted Proportional Fairness and Pricing for TCP”, submitted to ACM CCR. [6] Biddiscombe M., Midwinter J., Sabesan S., ’Application of free market principles to telecoms resource allocation.’, Electronics Letters vol35, no 4, Feb, 1999. [7] Bandwidth-X, URL: http://www.band-x.com. [8] RateExchange, URL: http://www.ratexchange.com. [9] Sairamesh, R., Dailianas, A., Gottemukkala, V., Jhingran, A., Kumar, M., Codella, C., ”E-Marketplaces: Architecture, Trading Models, and Their Role in Bandwidth Markets”, citeseer.nj.nec.com/249617.html.

RS:TVU

700000

600000

500000

RS TVU

400000

300000

200000 0

5 10 15 20 25 Number of demands per source-destination pair (mixed)

30

Inelastic-Elastic Users Proportion 10-90%

Fig. 5. Total Value Forwarded for all considered algorithms

ant termed FCFS 10 90 reserves 10% of resources for serving inelastic demands. We show in Graph-3, Graph-4 and Graph-5 the results for 60/40% proportion of inelastic/elastic users, 25/75% proportion of inelastic/elastic users and 10/90% proportion of inelastic/elastic users. Clearly DMLA outperforms all FCFS variants. There are two interesting points. As the traffic intensity increases the DMLA advantage increases (along x-axis) too. As the proportion of elastic users increases (along the 3 graphs) the competitive advantage of DLMA decreases. Both results are reasonable. In the first case the increase of traffic intensity increases the number of high priority demands that have an advantage in obtaining light-paths under DMLA. In the second case the increase of the elastic medium and low priority proportion of demands decreases the number of high-priority demands to be served that benefit more from an allocation. V. C ONCLUSIONS We have presented a new algorithm that performs dynamic light-path allocation in WDM networks and can be applied to any other optical network with resources of a discrete nature (like SDH networks). The algorithm is based on the idea of proportional fairness and addresses both elastic and inelastic demands. We have compared the algorithm with pre-planned alternatives and we have shown its advantages (up to 60% in out expreriments)-in terms of the total value of the traffic forwarded- a characteristic that makes it useful in applications where dynamic bandwidth provisioning is offered by multisevice optical carriers. VI. ACKNOWLEDGMENTS We would like to thank P. Hammer, D. Ireland and R. Kadengal for the endless discussions and comments they have been kind enough to provide us with. Thanks also to I.Sitaridou for helping with grammatical corrections of this document. This work has been sponsored partially by Nortel and an EPSRC CASE studenship.