Multipath Routing Mathematical Model to Solve the Traffic Engineering in Multi-Protocol Label Switching Network

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1 Journal of Computer and Communcatons, 2017, 5, ISSN Onlne: ISSN Prnt: Multpath Routng Mathematcal Model to Solve the Traffc Engneerng n Mult-Protocol Label Swtchng Network Han Attar Phladelpha Unversty, Jordan, KSA How to cte ths paper: Attar, H. (2017) Multpath Routng Mathematcal Model to Solve the Traffc Engneerng n Mult-Protocol Label Swtchng Network. Journal of Computer and Communcatons, 5, Receved: November 14, 2017 Accepted: December 26, 2017 Publshed: December 29, 2017 Copyrght 2017 by author and Scentfc Research Publshng Inc. Ths work s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY 4.0). Open Access Abstract Multpath Protocol Label Swtchng (MPLS) s a routng mechansm (technology) used n modern telecommuncaton networks, whch s bult as a mult-servce network wth a certan Qualty of Servce (QoS). To mantan the requred QoS n such complcated networks, the Traffc Engneerng (TE) should be equpped wth optmum traffc management, routng mechansm, and swtchng operatons, whch are what ths paper tackles, where the TE s dentfed as the optmal dstrbuton of flows n the exstng network. In ths paper, an effectve multpath routng mathematcal model s developed based on several prevous mechansms to ensure the guaranteed desred QoS and loadng balance accordng to the Telecommuncaton Network Systems (TCS) resources, to acheve the optmum TE, and hence mprovng the network usage effcency. Moreover, the obtaned mathematcal optmzaton algorthm results are provded through the relatve equatons. Indeed the developed routng mathematcal model n ths paper s sutable for the dynamc dstrbuton of nformaton flows, whch s the man mprovement n the TE acheved n ths work. Keywords Mult-Sources Network, Optmum Traffc Management, Routng Mechansm, and Multpath Routng Mathematcal 1. Introducton Modern telecommuncaton networks of the new generaton,.e., Next Generaton Network (NGN), n accordance wth the trend of the global communcatons ndustry, should be bult as a mult-servce network wth a certan Qualty of DOI: /cc Dec. 29, Journal of Computer and Communcatons

2 Servce (QoS) traffc polytypc users. Multpath Protocol Label Swtchng (MPLS) s a routng mechansm used to acheve the requred QoS n the modern telecommuncaton networks, where the traffc management, routng and swtchng operatons are consdered as the man parameters for the Traffc Engneerng (TE) concepts [1] [2], where TE s dentfed as the matter to optmze the dstrbuton of the network data flow. In [3], the QoS for hybrd telecommuncaton network s acheved by developng an adaptve routng method, where n [4] the optmum utlzaton for the resources of networks s nvestgated to acheve communcaton models accuracy that provdes the requred performance by mprovng the routng protocols. However, the network performance was mproved n dfferent ways than the routng methods, such as applyng network codng as n [5] [6] [7], whch shows that decreasng the number of the transmtted packets does mprove the telecommuncaton traffc sgnfcantly n dfferent applcatons such as wreless sensor network [5] [6], and long term evaluaton advance moble communcaton network [7]. General understandng and analyss for applyng network codng n cooperatve networks over lossy channels wth the mprovement of traffc s shown n [8] [9]. In [10], the author proposed rateless layered for multple descrpton vdeo delvery through a relay, and t showed as well how the proposed scenaro exploted the path delvery over a moble network to show the advantages of the relayng when the network s optmzed ntern of routng and the unequal error detecton. In ths paper, an effectve multpath routng mathematcal model s developed whch s derved from dfferent exsted multpath routng mechansms to ensure obtanng the desred QoS and loadng balance accordng to the Tele-Communcaton Systems (TCS) resources, and hence reachng the most effectve TE, whch s called the optmum TE. The optmum TE s the man requrement to mprove the network usage effcency. Accordngly, durng the wreless communcaton system where one packet can be smultaneously transmtted along multple paths, the optmum TE s provdng balanced loadng and helpng to mprove the TCR, especally hgh-speed and assocated lkelhood-tme qualty of servce ndcators. The rest of the paper s organzed as followng: n Secton 2, the multpath routng soluton general requrements s dscussed, wth the classfcaton of the mathematcal models of routng; Secton 3 provdes the requred back ground for Grafokombnatornye routng algorthms and models; Then, the mathematcal optmzaton algorthm s obtaned and ts theoretcal results are provded through the relatve equatons; and fnally, the paper concludes. 2. General Requrements for the Solutons of the Multpath Routng Problems Multpath routng requrements are lsted n two groups of demands: the frst DOI: /cc Journal of Computer and Communcatons

3 group of demands s devoted for any tradtonal routng algorthms whch are assumed to have low computatonal complexty, fast convergence and mnmum volumes of traffc generated by the servce; the second group of requrements s needed to ensure the desred QoS and load balancng TCS based on the mplementaton of the prevously mentoned prncples for the traffc management concepts. The Classfcaton of mathematcal routng models s deduced from the analytcal results of [11], whch provde the man approaches to the mathematcal modelng and solvng the multpath routng tasks. Fgure 1 shows the classfcatons of the mathematcal models and routng algorthm, whch s dvded n to two models; graph combnatoral (Grafokombnatornye routng) and streamng models. The bass of the graph models used n the mathematcal descrpton of TCS, as a drected or undrected graph, where both are usng combnatoral algorthms to search for the shortest paths or multpath between any gven pars of nodes (vertces) n the network. Flow models together wth the calculaton of the path routs numbers are used to formalze the requred user traffc dstrbuton decson problem along these routes. Due to the fact that the above routng algorthm requrements are regarded as contradctory; t s essentally mportant to propose a number of approaches for the purposes of formalzaton and solvng multpath routng tasks based on the use of varous mathematcal modelng and soluton algorthms, resultng n one form or another optmzaton problems, whch s the man goal of ths paper. As a result, the soluton of TE for MPLS-TE networks n the framework of a mathematcal model s mpossble to be obtaned by ust one optmum path routng that can be appled for all types of routng algorthms. As a result, a hybrd approach, combnng the approaches and algorthms that are typcal for dfferent routng models. 3. Grafokombnatornye Routng Algorthms and Models To solve the problem of fndng the shortest path for a gven TCR represented as a graph algorthms.e., Grafokombnatorny, several algorthms have been Fgure 1. Routng algorthms and mathematcal models classfcatons. DOI: /cc Journal of Computer and Communcatons

4 proposed such as Bellman-Ford, Dkstra and Floyd-Warshall as appled recently n [12] [13] n dfferent applcatons. The basc dea of the Bellman-Ford algorthm s to fnd the frst path length [14], whle Kratchayshh provded the path that contans not more than one arc n the shortest path length, and then the path that does not contan more than two arcs, etc. The chosen shortest path s the path that contans not more than h arcs wll be called the shortest ( h) means. Assume that node 1 s the source node, and t s needed to fnd the length of the shortest paths from ths source to the other nodes n the graph. It s known that the arc length (arc parameters) depends on the partcular task and t can be both postve or negatve. In the proposed scenaro; the negatve values can be calculated. Addtonally, the path column must not be cycles. Let D to be the length of the shortest path ( h) from node 1 to node, assume that D = 0 for all h. Fndng the shortest path conssts of several stages. In the frst stage of the algorthm; t should be: ( ) ( ) D h = for all 1 and D h = 0 (1) In the subsequent steps, each tme h 1 terates Bellman-Ford ( h) ( h 1 ) ( ) D = mn D h 1 + D for all 1 where D s the shortest path between the nodes and. The algorthm termnates when h reaches n, where n s the number of nodes n the network,.e., n the worst case, the tree of shortest routes s gven chan wth length of n 1 branches. The shortest path n the algorthm of Bellman-Ford becomes postve s because when the lengths of all arcs are postve (ntal D condtons for 1 may take any non-negatve numbers), the teraton Equaton (1) may be performed n parallel for dfferent nodes substantally randomly,.e., both synchronously and asynchronously. Another wdely used graph algorthm for fndng the shortest path s Dkstra s algorthm [12] [13] whch allows buldng a tree of the shortest dstances and paths from a gven node to all the others. The algorthm s applcable for orented, non-orented and mxed network graphs. Accordng to ths algorthm, the shortest among all the shortest paths from node s one arc length, whch connects ths node to the next adacent node. Snce each path conssts of several arcs; t wll always be longer path than the frst length of the arc due to the assumpton of the postvty of the arc lengths. The next shortest among Kratchayshh ways must be a way from one arc to the next nearest neghbor node, or the shortest route from the two arcs passng through the node selected n the frst step, etc. To descrbe ths process formally n the form of the algorthm, we assume that each node s labeled as D, meanng estmate the length of the shortest path from node. when the score becomes constant, we assume that the fnal node s marked. Formally, the algorthm operates as follows: 1 (2) DOI: /cc Journal of Computer and Communcatons

5 Intally, P = {1}, D 1 = 0 and D = D 1 for 1. Steps 1 (to fnd the next nearest node). Fnd P, such that D = mn D (3) P put P: = P {}. If P contans all the nodes, then the work n the algorthm ends. Step 2 (labels update) to put all P D : = mn D, D + d (4) Go to step 1. Snce the number of operatons performed by the Dkstra s algorthm at each step n proporton to N, where N s the number of the network nodes, and the steps terated N-1 tmes, the amount of computaton n the worst case s equal to N 2, nstead of N 3, lke Bellman-Ford algorthm. The advantages of these algorthms are relatvely the low computatonal complexty and ease of mplementaton. In the classcal formulaton of the algorthms presented problems are manly the shortest path from the source node to any ntermedatng node tll reachng the recpent, takng nto consderaton that the problem of ET routng strategy s needed, whch would enable to balance the load on the network and to take nto account the requrements for QoS of the processed streams. In addton, one of the requrements for routng protocols n the MPLS-TE networks s the possblty remarshrutzats traffc for a tme not exceedng 50 ms, whch mples a prelmnary fndng of crcumventon, and (backup) paths. As a result, the deas contaned n the Bellman-Ford algorthms and Deyktry, were developed n the mathematcal models and multpath routng algorthms. Multpath routng strateges have been developed, whch are based on graph-lad combnatoral algorthms to fnd the shortest paths. The most famous practcal mplementaton are the algorthm for ECMP (Equal Cost Load Balancng), expandng the capabltes of RIP (Routng Informaton Protocol) and OSPF (Open Shortest Path Frst), plus load balancng algorthms along paths wth dfferent value presented n the company s propretary protocols IGRP (Interor Gateway Routng Protocol) developed by CISCO and EIGRP (Extended Interor Gateway Routng Protocol). In each of these protocols; t s mplemented the same approach to solve the routng problem, whch s generally reduced to an algorthm of three actons as follows: 1) Fndng the set of shortest paths; 2) Selectng routes for handlng loads wth the same or dfferent value; and 3) The load dstrbuton on the selected paths are usually proportonal to the matrc. A further development of the dea of usng Grafokombnatornyh models are algorthms for fndng the set of shortest paths to address multpath routng problem. For example, the dea of a dstrbuted algorthm for multpath routng M-path [15] s to fnd the routng graph that does not contan loops and presented the set of arcs are gven n Equaton (5): DOI: /cc Journal of Computer and Communcatons

6 {(, ) m, } where M s the pluralty of network nodes, M s the pluralty of nodes neghborn, s the node, and node to node k. SG = m n n S m M (5) m S s the varety of optons subsequent packets from The shortest multpath, accordng M-path, s gven by Equaton (6): { } S = k M D < D (6) k where D k s the local value of the shortest path tree from node to k. Then the elmnated loops are acheved by makng the followng condtons whch are gven n Equaton (7) and Equaton (8): ( ) ( ), FD t D t k M (7) k { } ( ) ( ) ( ) S t = k M D t < FD t, (8) k where FD s the calculaton of the allowable dstance set S. M-path algorthm ensures that the achevement of equalty s gven n Equaton (9): k FD = D = D,,, k M (9) An alternatve approach to solve the problem of mult-path routng algorthm s mplemented n DASM (Multpath Dstance-Vector Algorthm) [16] [17]. Ths algorthm assumes that each ntermedate router contans the record routng table, whch ncludes a set of parameters for each destnaton host. In addton, each such record conssts of several parameters that determne the next router on the path to the destnaton node and the dstance along the path that does not contan loops. Accordng to the algorthm, each router can be n one of two states: ether actve or passve. The router s regarded as passve when all paths S derved from the exchange, whch means that all ts neghbors are lsted n the routng table. Otherwse, the router becomes actve; and hence starts tryng to fnd a path to the node by sendng query messages to neghbors. The shortest path between nodes and n DASM wll be determned by the expresson proposed n the dstrbuted Bellman-Ford algorthm as gven n Equaton (10): { k k } Dmn = mn D + l k M (10) where l s the length (cost) of the transton towards a neghbor k; f k s the k neghbor s no longer avalable l, use the value. The resultng multpath S k s gven by Equaton (11): * S = k M D < mn FD, D (11) { ( mn )} k * where D k s the upper lmt of the neghbor k to the node wth dstance, and FD s the allowable dstance from the router to router. Accordngly, resultng multpath contans loops S the condton becomes as n Equaton (12): S t = k M D t < FD t (12) { } ( ) ( ) ( ) k DOI: /cc Journal of Computer and Communcatons

7 It should be noted that, despte of the fact that the algorthms and MPATH DASM for fndng shortest paths usng dfferent approaches (n the frst case, t s Dkstra s algorthm, whle the second case s the dstrbuted algorthm of Bellman-Ford), the condtons of the loops absence n the above algorthms are stll dentcal. Another development of the multpath algorthm of Bellman-Ford s the ROAM (Routng On-Demand Acyclc Multpath). The feature of ths algorthm s ts ablty to store the router nformaton only about the paths to the purpose of the currently produced transmsson packet. Ths mnmzes the amount of nformaton stored n the ntermedate devce, whch s partcularly mportant n the case of large networks. Path to the remote nodes are determned on demand when recevng a packet from a node whch has no drect path wth node. Table of dstances n the router s a matrx contans the dstance to each destnaton node D k from a neghborng node k, and the response status flag ST k. Table routng s a vector comprsng for each destnaton node that s located n dstance to the destnaton, the allowable dstance FD, message dstance RD,used route s, the requester and the flag o tmestamp T. Table values channel ncludes the cost of channels to known neghbors k for assembly s l. k Accordng to the algorthm ROAM [18], the router becomes n one of the followng three states: 1) Passve: The nformaton about the exstence of the recpent s ether known or unknown; 2) Actve: The watng for nformaton on n the process of creatng a route; or 3) Actve-watng: Actve and watng for a response from the neghbors of the most recommended or expected destnaton. In the passve state; the router takes the shortest route only from all avalable nodes, accordngly, the alternatve routes va neghbor q M can be selected as the prmary under the condtons of Equaton (13), and Equaton (14): ( ) ( ) ( ) { } D t + l t = mn D t + l, x M (13) q q q x x * ( ) < ( ), where FD ( t) D ( t) D t FD t = (14) The algorthm guarantees the absence of loops n the selecton of alternatve routes to node, when the topology router can be set to swtch nto an actve state, n whch updates are exchanged by dffuson n order to fnd the man route. Along wth the aforementoned advantages Grafokombnatornyh models and algorthms, t s worth notng a number of mportant shortcomngs, greatly lmtng ther practcal mplementaton n today s mult-tcs, whch are: Frst: The agreed soluton of problems of load balancng, QoS routng and securty n the framework of graph models and combnatoral algorthms, optmzed for DOI: /cc Journal of Computer and Communcatons

8 sngle-commodty-pole network, the ncreasng number of traffc (products) on the network faces a number of serous dffcultes descrptve and computatonal nature, snce t s assumed that all network resources are allocated one under consderaton traffc. Second: The man advantage of the models consdered, consstng n smplcty and predctable computatonal complexty of mplementaton, wth the number of parameters taken nto account QoS (three or more), t s reduced to zero, because the task of fndng even one of the shortest path n ths case becomes completed. It should be noted that the decson to route tasks orgnally dd not ft nto the framework of Grafokombnatornyh models, snce they do not allow the correct mathematcal descrpton of the dynamcs of the processes status, provdng multple servces and guaranteed qualty of communcaton over the two ndcators. In modern condtons the search for the shortest path (multpath) for each of the servced traffc s not always even necessary, but the more suffcent, condton for the successful soluton of routng problems, snce, stll remans an open queston of the allocaton of resources along each of the routes. At a tme when the decson block of problems s dffcult, and sometmes almost mpossble to cover a countable number of optons; the use of combnatoral algorthms becomes mpractcal, or use them n conuncton wth other search methods. Ths s partcularly true for applcatons n whch, the network settngs s expected, so, t s needed to consder many external factors, such as the parameters of the nformaton flows. Despte of the lmted opportuntes Grafokombnatornyh mathematcal models; the lack of strct requrements to the qualty of decson-route tasks prevously contrbuted to the wde dssemnaton of such algorthms. In ths regard, graph models and algorthms for combnatoral Mller-Morta-Mumford (MMM) can only be vewed as temporary (ntermedate) step between realzed n practce and promsng solutons n meetng the complex demands made to the multservce TCS. 4. Conclusons The man task, whch s proposed n the traffc engneerng (TE) concept s the optmal loadng of all sectons of the network to mprove the effcency of network usage. Ths requrement mples the use of traffc through several mechansms avalable paths network. Thus, the successful soluton of the problem of engneerng traffc n multservce networks depends on the used routng mechansms. An analyss of multpath routng models [11] [18] hghlghted the two-class models graph and streamng. As shown by the analyss, wthn each class of mathematcal models exst multpath models that nvolve free resources on the network to servce the traffc. Ths allows more effcent use of avalable network resources. Analyss of protocol solutons used n modern Tele-Communcaton System (TCS), showed that the practce receved a graph model, mplemented n the DOI: /cc Journal of Computer and Communcatons

9 RIP, OSPF, EIGRP. These models offer the smplcty and low computatonal complexty. However, the lmtatons of the solutons obtaned and a one-way orentaton s not currently allowed effectve use of all avalable network resources. These dsadvantages can be overcome wth the help of the latest developments [19] [20] n the framework of graph models, allowng you to extend the scope of these algorthms. Usng streamng routng models can dstrbute traffc over the network and use the resources avalable. Implementaton complexty assocated wth a large amount of sgnal nformaton and the potental nstablty of the routng algorthm for changng traffc characterstcs, resulted n the absence to date of protocol mplementaton decsons based on ths class of algorthms. At the same tme, despte the lack of mplementaton of the protocol on the bass of flow routng models, the demands put forward to modern multservce TCS may meet only wth the use of ths class of algorthms. The proposed analyss n ths paper shows that the full TE problem cannot be solved usng the approaches proposed n only one of the classes, whch means that the acheved solutons are ether as graph [21] and [22], although they do not take nto account the possblty of flow dstrbuton or streamng [15] and whch only solves the problem of flow dstrbuton. Obvously, for the dynamc dstrbuton of nformaton flows, these solutons are not sutable. References [1] Awduche, D.O. and Ban J. (2002) Internet Traffc Engneerng Usng Mult-Protocol Label Swtchng (MPLS). Computer Networks, 40, [2] Awduche, D., et al. (2002) Overvew and Prncples of Internet Traffc Engneerng. No. RFC [3] Alhh, M., Attar, H., Samour, M. and Akulynchev, A. (2017) Researchng the Impact of Parameters of the Developed Routng Models on Network Performance. Studes n Engneerng and Technology, 4, [4] Alhh, M. (2017) Settng an Optmzaton Problem of Dstrbutng Traffc across Multple Independent Paths. Transactons on Networks and Communcatons, 5, [5] Attar, H., Vukobratovc, D., Stankovc, L. and Stankovc, V. (2011) Performance Analyss of Node Cooperaton wth Network Codng n Wreless Sensor Networks. 4th IFIP Internatonal Conference on New Technologes, Moblty and Securty, Pars, 7-10 February 2011, [6] Attar, H., Stankovc, L. and Stankovc, V. (2014) Cooperatve Network-Codng System for Wreless Sensor Networks. IET Communcatons, 6, [7] Attar, H., Stankovc, L., Alhh, M. and Ameen, A. (2014) Determnstc Network Codng over Long Term Evaluaton Advance Communcaton System. 4th Internatonal Conference on Dgtal Informaton and Communcaton Technology and Its Applcatons (DICTAP), Bangkok, 6-8 May 2014, DOI: /cc Journal of Computer and Communcatons

10 [8] El-Hh, M., Attar, H., Solyman, A. and Stankovc, L. (2016) Network Codng Cooperaton Performance Analyss n Wreless Network over a Lossy Channel, M Users and a Destnaton Scenaro, Communcatons and Network, 8, [9] Attar, H. (2017) Data Combnaton over Physcal Layer Usng Network Codng wth PUM Turbo Codes. Journal of Computer and Communcatons, 5, [10] Nazr, S., Stankovc, V., Attar, H., Stankovc, L. and Cheng, S. (2013) Relay-Asssted Rateless Layered Multple Descrpton Vdeo Delvery. IEEE Journal on Selected Areas n Communcatons, 31, [11] Lemeshko, O.V., Halan, A.M. and Starkova, O.V. (2011) Mult-Level Traffc Management n the MPLS-TE DffServ Network. 11th Internatonal Conference the Experence of Desgnng and Applcaton of CAD Systems n Mcroelectroncs (CADSM), [12] Waleed, S., Fazan, M., Iqbal, M. and Ans, M.I. (2017) Demonstraton of Sngle Lnk Falure Recovery Usng Bellman Ford and Dkstra Algorthm n SDN. Internatonal Conference on Innovatons n Electrcal Engneerng and Computatonal Technologes (ICIEECT), Karach, 5-7 Aprl 2017, [13] Dela Cruz, J.C., Magwl, G.V., Mundo, J.P.E., Gregoro, G.P.B., Lamoca, M.L.L. and Vllaseñor, J.A. (2016) Items-Mappng and Route Optmzaton n a Grocery Store Usng Dkstra s, Bellman-Ford and Floyd-Warshall Algorthms. IEEE Regon 10 Conference (TENCON), Sngapore, November 2016, [14] Awerbuch, B., Bar-Noy, A. and Gopal, M. (1994) Approxmate Dstrbuted Bellman-Ford Algorthms. IEEE Transactons on Communcatons, 42, [15] Ben-Ameur, W., et al. (2001) Routng Strateges for IP Networks. Telektronkk, 97, [16] Leduc, G., et al. (2006) An Open Source Traffc Engneerng Toolbox. Computer Communcatons, 29, [17] Skvée, F., Balon, S. and Leduc, G. (2006) A Scalable Heurstc for Hybrd IGP/MPLS Traffc Engneerng Case Study on an Operatonal Network. IEEE Internatonal Conference on Networks (ICON), Vol. 2, Sngapore, September 2006, [18] Abu-Al, N., Mouftah, H.T. and Gazor, S. (2005) Mult-Path Traffc Engneerng Dstrbuted VPLS Routng Algorthm. Proceedngs of Systems Communcatons, August 2005, Montreal, [19] Natale, D., et al. (2003) Inter-Area Traffc Engneerng n a Dfferentated Servces Network. Journal of Network and Systems Management, 11, [20] Chang, L.-H., et al. (2013) QoS-Aware Path Swtchng for VoIP Traffc Usng SCTP. Computer Standards & Interfaces, 35, [21] Vutukury, S. and Garca-Luna-Aceves, J.J. (2001) MDVA: A Dstance-Vector Multpath Routng Protocol. Twenteth Annual Jont Conference of the IEEE Computer and Communcatons Socetes, Anchorage, AK, Aprl 2001, [22] Vutukury, S. and Garca-Luna-Aceves, J.J. (2001) MPATH: A Loop-Free Multpath Routng Algorthm. Elsever Journal of Mcroprocessors and Mcrosystems, 24, DOI: /cc Journal of Computer and Communcatons