The Scalability and Performance of Common Vector Solution to Generalized Label Continuity Constraint in Hybrid Optical/Packet Networks

Transcription

1 The Scalability and Performance of Common Vector Solution to Generalized abel Continuity Constraint in Hybrid Otical/Pacet etwors Shujia Gong and Ban Jabbari {sgong, George Mason University bstract In hybrid Otical/acet networs, wavelength and V tag continuity along a abel Switched Path are two common constraints These two tyes of constraints, referred to as Generalized abel Continuity Constraints, have global significance in a networ; namely, the label should aear only in other lin- or node- disjoint aths In considering these constraints, a solution is the common vector aroach, which sees a common available label along the ath determined by CSPF without label constraints In this aer, we rovide an estimation method to comute the uer bound of the blocing robability for the above aroach We also address the scalability roblem of the existing traffic engineering algorithms We then resent the simulation results corroborating with our analytical modelh I ITRODUCTIO Traffic engineering utilizing Multi-Protocol abel Switching (MPS) and Generalized MPS (GMPS)[] are widely utilized in the bacbone of the Internet infrastructure [] GMPS is attractive as it allows end-to-end control, rovisioning, rotection and restoration in the hybrid IP and Otical transort networs onetheless, there are challenging roblems associated with the abel Switched Path (SP) setu rocess due to hysically diverse data forwarding lane with multile routing and switching technologies The ath comutation algorithms are needed to tae into account of all forwarding technology and networ secific constraints in order to yield an end-to-end SP n examle of the above constraints is the wavelength continuity constraint in ll-otical etwors (Os) or networs based on Reconfigurable Otical dd-dro Multilexer (RODM) and/or Dense Wavelength Division Multilexing (DWDM), in which an end-to-end SP needs to be setu Deterministic networ services to high-end escience alications that require high seed and high caacity lightath, which is subject to the wavelength continuity constraint, are in demand nother examle is the V tag continuity, where an endto-end ath across geograhically disersed Ethernet switches is needed This Ethernet switching technology is deloyed not only in local area networs, but also in bacbones such as in the hybrid otical and acet networ infrastructure, eg, HOPI roject Ethernet switches in the networ may not necessarily suort V tag swaing and therefore, V tag continuity constraint also needs to be satisfied Both wavelength and V tags, as mentioned above, are labels These as well as other labels can be classified under Generalized abel Continuity Constraints (GCC) GMPS defines a set of rotocols as the standardized control lane to instantiate the SP setu, tear-down and maniulation In this aer, we discuss the alicability of a common vector solution to address the GCC roblem We develo an analytical model to obtain the estimation on blocing robability of SP setu requests We also develo a simulation model Subsequently, numerical results are resented and comared with the analytical model Finally, concluding remars are made II COMMO VECTOR SOUTIOS TO GCC COSTRITS n aroach to solve the wavelength continuity constraint by converting a etwor Grah to a Wavelength Grah has been resented in [3] In wavelength grah, one lane is generated for each wavelength, and each node in the networ grah is dulicated at each wavelength lane For those nodes that have wavelength conversion caability, additional lins are created to connect the relications of each node on corresonding wavelength lane Virtual nodes are generated as a dummy originating node and a dummy destination node These virtual nodes are connected to the relications of the true originating node and destination node resectively and metric on those virtual lins is assigned as zero lthough wavelength grah can find an otimal ath for an SP setu request, and can liewise be used to address V continuity constraints, it has inherent scalability roblems The comutational comlexity of wavelength grah is n(n + ), where is the number of wavelength in a fiber and n is the number of nodes in the networ grah, which maes it imractical for large label sace regardless of the networ size V Tag Constraints and the Solution V tag is a field of bits, which can identify 4096 Vs If we create V lane as we do on wavelength lane and relicate nodes and lins, a networ will generate hundreds of millions of nodes and lins Clearly, wavelength grah aroach cannot rovide a scalable solution to V tag continuity constraint To address this roblem, we utilize the Common Vector solution, where the elements of the vector reresent the availability or the lac of the labels at a node across the ath The set of available labels can simly be determined by taing

2 the logical D across the vectors at each node on the ath method such as Extended Indexing Ref [4] can be used to facilitate the distribution of the labels vector comrised of 4096 bits, with each bit indicating the status of one of the 4096 V tags used at each node is an attractive solution for large Ethernet networs in ractice B Modeling of Common Vector Solution to Wavelength Continuity Constraint In this section, we show that the common vector aroach is a reasonably good solution to wavelength continuity constraints by the following models We assume that the arrival rocess of SP setu requests to each node is Poisson with mean of λ and the dearture rocess is exonential with mean service time /μ We use the following notations in our model: G <V, E>: etwor grah G with node set V and lin set E : Total number of nodes in V M: Total number of lins in E : Total number of labels in each lin In this context, labels are wavelengths v i : ode i in node set V, where i e i : in i in lin set E, where i M h : The number of hos of the shortest ath between v i and v j in G λ : The intensity of traffic with v i and v j as source and destination node, resectively f : The traffic flow generated by λ in the networ fe : The total traffic flow on lin e I(v i, v j, e ): n indication function on whether the shortest ath between v i and v j on the networ grah traverses lin e e i : The number of available labels on lin e i P : Path between v i and v j : The lin that the m th ho along P traverses m,, m : The number of labels that are commonly available on the first m hos along P We also assume that the traffic intensity in the networ is not high When an SP request arrives at node vi, vi will chec its Traffic Engineering Database (TEDB), rune those lins without enough bandwidth and run CSPF without considering the label availability fter a ath is found, vi will erform the logical D oeration on the vector of label availability along the ath If no commonly available label is found, the SP request will be rejected To simlify the analysis, we assume that the label occuancy on each lin is indeendent This is not an accurate assumtion in that all the labels along an SP ath are selected to be the same, which indicates the deendency of the label occuancy on different lins However, this deendency favors the common vector solution, and the actual erformance of the networ will be better than the analytical model we rovide in the next subsections C Estimation of the umber of vailable abels on a in Blocing robability in various networ scenarios have been extensively studies, such as in [5] [7] Comuting the number of available labels on a lin is a M/M/m/m queueing roblem We first need to now the traffic flow on each lin The traffic flow generated by any air of nodes vi and vj is: f λ h () We first run the shortest ath first algorithm between each air of nodes on a networ grah without traffic and define: if P traverses e ; I( v, v, e ) () i j 0 Otherwise Due to the assumtion that the traffic intensity is not high, only a small roortion of SPs will tae a ath other than the shortest one, and we can neglect the difference between the offered load and the carried load on a lin Therefore, fe can be estimated as: fe i j f I( v, v, e ) (3) With the assumtion of light traffic intensity, we can also aroximate the arrival of SP requests to a lin to be a Poisson rocess Therefore, we can aly M/M/m/m formula to find the number of available labels f /! (4) f / j!) ei e ) i j ( 0 This estimation in Equation (4) is very rough esecially when traffic intensity is moderate It assumes static routing and overestimates the traffic flow on each lin Reference [8] rovides a more accurate estimation on the uer bounds of lin blocing robability in homogeneous otical ring networs If we assume that the routing algorithm is dynamic, the lin blocing robability is nearly the same in the whole networ, and the networ is comlicated enough that the alternative ath is of the equal length as the shortest ath, we can further simlified the equation (3) as follows: f i j fe (5) M Because we use offered load instead of carried load to calculate the traffic flow on each lin, the equation (4) definitely gives us the uer bound of the actual blocing ratio D Estimation of Blocing Probability of SP Setu Requests Equation (4) gives the robability of e i ) For an SP with multi-hos, a successful connection needs at least one articular label that is commonly available along the ath Given a two-ho SP P between v i and v j, we denote that there are common wavelength available on and as, ) j ei

3 Given and, we have:, P ) (,, P P 0 0 (6) P ) P ) P )) Given labels in a lin, the number of ossibilities for and is: Given labels in a lin, (7) and,, means that we choose out of on first Because there are common labels on and, it means that we choose labels out of labels on and - labels out of - labels on Fig etwor Toology The number of ossibilities is: (8) Dividing (8) by (7), we have: P, (, ) P P P where max(0, + -) min(, ) Therefore, we have:, P ) P where max(0, + -) min(, ),, (9) P ) (0) The estimation of the case that there are common labels along a n-ho SP is an iterative rocess We have:,,, n P ),, n P (,,, n n, P P 0 0 () ),, n P ) n P )) Fig Comarison of Estimated and ctual Blocing Therefore, the robability of blocing is P 0) (,,, n P We assume that the alternative ath between any air of nodes v i and v j is of the same length as the shortest ath The exected blocing robability is as follows: λ P b P (,,, h P λ 0) () If we use (3) to estimate the traffic flow on a lin, we called it estimation based on static routing If we use (5) to estimate the traffic flow on a lin, we called it estimation based on homogeneous lin load assumtion III SIMUTIO VERSUS YTIC RESUTS We consider a networ toology as deicted in Fig, and assume that the traffic matrix is homogeneous We consider that each lin has 8 wavelengths Fig shows the estimation of blocing robability based on both static route and the homogeneous lin load assumtion resectively It also showed the actual blocing robability by simulating 0 million SP setu requests We can clearly see

4 Fig 3 Comarison of ctual Blocing in Wavelength Grah Solution and Common Vector Solution Fig 4 Comarison of Time Consumtion that the estimation based on homogeneous lin load assumtion is closer to the actual blocing rate Both estimations are uer bounds of the actual blocing rate Figure 3 also comared the blocing ratio of the common vector solution with the wavelength grah solution Given incoming traffic to each node of 3 Erlangs, we simulated the cases that there are 4 to 8 wavelengths in a fiber one of the node has wavelength translation caability The wavelength grah solution can accet more calls than the common vector solution However, when the networ load is very high or very low, the imrovement on the call accetance ratio is not significant When the networ load is moderate, wavelength grah solution can show its advantage with regard to call accetance The comutational comlexity of the common vector solution is equivalent to run Dstra algorithm and then find the availability of labels on each lin traversed by the SP Therefore, it is O(M+log())+O( +) The comutational comlexity of the wavelength grah solution is given in [3], which is O(( + )) Figure 4 shows that the comutational comlexity of common vector solution is almost irrelevant to the number of wavelengths on a lin, while the wavelength grah solution shows that even if the wavelength number is small, it still taes much more time than the common vector solution does Homogeneous and non-homogeneous traffic matrix may result in different networ blocing scenario To mae the comarison, we design three cases: ) Traffic generated at each node is the same and the traffic matrix is homogenous; ) Traffic generated at each node is the same and the traffic matrix is non-homogenous, ie the mean holding time between node vi and vj is in roortion to the value in i th row and j th column given in table I; and 3) Traffic generated at each node is in roortion to the values given in table II and the traffic matrix is nonhomogenous as given in table I Fig 5 Comarison of Blocing Probability of Common Vector Solution between Case, and 3 TBE I O-HOMOGEEOUS TRFFIC MTRIX node TBE II O-HOMOGEEOUS TRFFIC MTRIX WITH O- HOMOGEEOUS TRFFIC ITESITY T ECH ODE node Traffic Intensity

5 Fig 6 Comarison of Blocing Probability of Wavelength Grah Solution between Case, and 3 Fig 7 Estimated vs ctual Blocing Probability of Common Vector Solution in Case, and 3 Figure 5 and 6 show the blocing robability of all the three cases of the common vector and wavelength grah solutions resectively Comaring case and case, there is not much erformance degradation However, case 3 is clearly worse than case and case This imlies that given the same traffic intensity, a networ with nearly homogeneous traffic demand has better erformance from blocing robability ersective Figure 7 shows the comarison between estimated and actual blocing robability of the common vector solution The estimations based on both equation (3) and (5) are showed When the traffic load is light, the estimation of blocing ratio based on dynamic routing is even less than the actual blocing ratio This is because the dynamic routing assumtion hides the non-homogeneous traffic demand from each node IV COCUSIO In this aer, we roose a scalable solution to the generalized label continuity constraints in an otical/acet hybrid networ We demonstrate that we can estimate the uer bound of the lin blocing robability and show that this scalable solution will only slightly degrade the Quality of Service from the call blocing ersective, esecially when the traffic load is light or the networ is overloaded This algorithm has been imlemented in the DRGO (Dynamic Resource llocation in GMPS Otical etwors) roject, an SF sonsored research to create dynamic, deterministic, and manageable end-to-end networ transort services for high-end e-science alications REFERECES [] E Mannie and Ed, Generalized multi-rotocol label switching (GMPS) architecture, RFC3954 [] D wduche and B Jabbari, Internet traffic engineering using Multi- Protocol abel Switching (MPS), Journal of Comuter etwors, vol 40, no, 9, Set 00, invited Paer [3] I Chlamtac, Faragoe, and T Zhang, ightath (Wavelength) routing in large WDM networs, IEEE JSC, vol 4, no 5, June 996 [4] B Jabbari, Extended indexing method for resource assignment, Internal Reort, ug 006 [5] R Barry and P Humblet, Models of blocing robability in allotical networs with and without wavelength changers, IEEE Journal on Selected reas in Communications, vol 4, no 5, , June 996 [6] W Chen and E Modiano, Efficient routing and wavelength assignment for reconfigurable wdm ring networs with wavelength converters, IEEE/CM Transactions on etworing, vol 3, no, 73 86, Feb005 [7] S Subramaniam, M zizogelu, and K Somani, ll-otical networs with sarse wavelength conversion, IEEE/CM Transactions on etworing, vol 4, no 4, , ug 996 [8] S Gong and B Jabbari, in erformance bounds in homogeneous otically switched ring networs, IEEE GOBECOM, San Francisco, ov 006