Network reliability analysis for 3G cellular topology design

Transcription

1 Soglaaari J. Sci. Techol. 3 (3, 63-69, May - Ju. 00 Origial Article Networ reliability aalysis for 3G cellular toology desig Chutima Promma* ad Ealu Esoo School of Telecommuicatio Egieerig Suraaree Uiversity of Techology, Naho Ratchasima, Thailad Received 8 Setember 007; Acceted 6 Jue 00 Abstract Networ reliability is a imortat issue i the toological desig of the 3G cellular etwors i order to guaratee cosistet services. This aer aims to reset etwor reliability aalysis of various etwor toologies, icludig saig tree, sigle rig, multirig, ad two versios of hybrid rig-ad-tree. We derived reliability aalysis models for the hybrid rig-ad-tree toologies i terms of the oeratioal robability of the etwor lis. The relimiary results show that the etwor reliability of the hybrid multirig-ad-tree toologies is 6.78% ad 3.78% higher tha that of the saig tree ad the sigle rig toology, resectively, while it is oly about 37.3% less tha that of the ure multirig toologies. Keywords: etwor reliability, toological etwor desig, 3G cellular etwors. itroductio Third geeratio (3G cellular etwors are beig deloyed throughout the world to suort voice, data ad multimedia services at high commuicatio seed. Networ desigers eed well-desiged etwor toologies to carry various ids of traffic ad guaratee the uality of the services i the 3G cellular etwors. To rovide uiterruted services, etwor desigers must ay secial attetio to etwor reliability issues, esecially the reliability of etwor toology. The etwor reliability is defied as the robability that the odes i the etwor ca commuicate with others ad the etwor toology is defied as the hysical itercoectios betwee odes i the etwor. Otical fiber cables, coer wired cables or microwave lis may be used to itercoect the odes. Cosiderig a 3G cellular etwor, it cosists of a set of radio access etwor subsystems (RNS coectig to the core etwor (CN, which cosists of servig GPRS (Geeral Pacet Radio Service suort ode (SGSN, ad gateway GPRS suort ode (GGSN. Each RNS cosists of a radio etwor cotroller (, which cotrols the radio resources ad services ad oe or more access oits called Node B or radio base statios (. Each trasmits/receives data traffic to/from mobile statios (MS i the cell site. These traffic demads go through lis betwee ad ad are aggregated ito higher caacity lis to the SGSN/GGSN. The etwor desigers aim to itercoect these comoets i the 3G cellular etwors ad esure that they ca commuicate i case ay Networ reliability ca be comuted by usig the oeratioal robability of the etwor comoet. The oeratioal robability is defied as the ercetage of time that the etwor comoet maitais its fuctios. It is the ratio of the meatime-betwee-failure (MTBF to the sum of the MTBF ad the mea-time-to-reair (MTTR. The MTBF ad MTTR ca be measured by the etwor moitorig system. * Corresodig author. address: cromma@sut.ac.th

2 6 C. Promma & E. Esoo / Soglaaari J. Sci. Techol. 3 (3, 63-69, 00 a. saig tree toology b. sigle rig toology c. multirig with three-cycle toology d. multirig with commo-ode toology e. hybrid sigle rig-ad-tree toology f. hybrid multirig with three-cycle-ad-tree toology g. hybrid multirig with commo-ode-ad-tree toology Figure. Networ toologies. sigle li failure occurs (Harmatos 00. Several studies existig i the literature addressig the etwor reliability issues to rotect the etwor i case of a sigle li failure. Ja (99 derived reliability models for three differet etwor toologies, icludig the saig tree, the sigle rig, ad the multirig with three cycles (Figure a-c. The author showed that the multirig with threecycle toology yields the highest etwor reliability amog

3 C. Promma & E. Esoo / Soglaaari J. Sci. Techol. 3 (3, 63-69, the three toologies. The reaso is that i case of failure more sare lis i the three-cycle toology ca be formed tha that of the saig tree ad the sigle rig toology. Charsriiyo et al. (00 roosed the use of multirig with commo-ode toology (Figure d for the wireless access etwors ad reseted reliability models for such toology. Although the multile-rig toology could result i high etwor reliability, it may be imossible to always build the etwor with this toology because the geograhical restrictio such as moutais or laes could reuire higher cost i costructig the rig toology. Billioet et al. (005 roosed the use of sigle rig toology for radio mobile access etwors. I fact, the reliability of the sigle rig toology is less tha that of the ure multirig toology. Devaraj et al. (00 roosed the saig tree toology for data commuicatio etwor desig. However, the saig tree toology is vulerable to failure ad has miimum etwor reliability because there is o bac-u ath i the saig tree toology. I case ay li failure, the commuicatio betwee odes i the etwor could be lost. I this aer, we reset the etwor reliability aalysis of the hybrid toologies for 3G wireless access etwors. We cosider two tyes of the hybrid toologies, the hybrid sigle-rig-ad-tree ad the hybrid multirig-ad-tree, because these toologies are more ractical i some etwor eviromet where the geograhical obstructio may exist. The hybrid sigle-rig-ad-tree is a toology cosistig of oe rig ad the remaiig odes form a saig-tree toology. The hybrid multirig-ad-tree is a toology cosistig of several rigs ad the remaiig odes form a saigtree toology. Usig grah theory, we derived the etwor reliability model for the hybrid toology ad comared with other toologies, icludig the saig tree, the sigle rig, the multirig with three-cycle, the multirig with commo-ode. The hybrid toology is a alterative aroach that allows relaxatio o formig the etwor toology where i ractical etwor istallatio oe might face geograhical restrictios or budget limitatios o etwor costructio. To the best of the authors owledge, the study o the etwor reliability of the hybrid toology has ot bee reseted. The secod art of the aer is orgaized as follows. I Sectio, we mathematically derive etwor reliability models for the hybrid rig-ad-tree toology. I Sectio 3, our relimiary aalysis results, which comare the reliability of various etwors, are reseted. Fially, Sectio rovides coclusio ad describes o-goig wor.. Networ Reliability Model Let a grah G(V, E reresets cellular etwors, i which V is the set of odes, which are the comoets i the 3G cellular etwor ad E is the set of edges. We assume that all odes are erfectly reliable but edges may wor with the robability or fail with the robability (-. All edge failures are assumed to occur ideedetly of each other. The etwor reliability of G is deoted by R(G, which is the robability that all odes i G ca commuicate with each other. Let V is the umber of odes i the etwor. Let us first review the existig etwor reliability models. Ja (99 reseted reliability models for the saig tree (G st, the sigle rig (G r, ad the multirig with three-cycle (G mr-3c toology as follows (details i aedix: R(G st ( R(G r ( R(G mr-3c ( 3 ( ( ( ( Note that Euatio (3 is the reliability model for the otimal multirig with three-cycle toology i which the mai rig is searated ito two sub-rigs by a ath (C h, the commo-edges of the two sub-rigs. I the otimal cofiguratio, the ath C h cotais (+/3 edges ad the two subrigs cosist of a eual umber of odes (Ja 99 (see aedix for a detailed derivatio. Charsriiyo et al. (00 reseted the reliability model for the multirig with commo-ode (G mr-c toology. It is writte as R(G mr-c (3 m i i { i ( } ( i where m deotes the umber of sub-rigs excludig the mai rig, i deotes the umber of odes i i th sub-rig, ad deotes the umber of odes i the mai rig. I this aer, we roose ew etwor reliability models for the hybrid sigle rig-ad-tree ad the hybrid multirig-ad-tree toology as follows:. Hybrid Sigle Rig-ad-Tree The hybrid sigle rig-ad-tree toology (G h-sr-t cosists of the mai rig coectig the umber of odes i the etwor ad the saig trees coectig the remaiig odes to the mai rig as show i Figuree. Note that the remaiig odes that are ot i the mai rig ca form more tha oe saig trees. Let m deotes the umber of odes i the mai rig ad deotes the umber of edges i the saig trees. We derive the etwor reliability for the hybrid sigle rig-ad-tree as follows: R(G h-sr-t (Pr[all m edges i a rig are oeratioal] + Pr[m- edges i a rig are oeratioal ad oe edge fails] Pr[ edges i saig trees are oeratioal] Ulie the sigle rig toology i which all odes i the etwor form oe rig, the ure multirig toology is the toology cosistig of several itercoected rigs of odes.

4 66 C. Promma & E. Esoo / Soglaaari J. Sci. Techol. 3 (3, 63-69, 00 We obtai R(G h-sr-t ( m m m (. Hybrid Multirig-ad-Tree The hybrid multirig-ad-tree toology cosists of a umber of rigs ad the saig trees coectig odes that are ot i the rigs. The rigs i the toology ca form i several ways. Here we cosider two ids of the multirigs that aear i literature; the multirig with three-cycle ad the multirig with commo-ode... Hybrid Multirig with Three-Cycle-ad-Tree I the hybrid multirig with three-cycle-ad-tree toology (G h-mr3c-t (Figure f, the rigs are i the form of three cycles i which the mai rig cosists of odes ad the ath addig to the rig cotai 3 edges. The saig tree cosists of edges. We derive the etwor reliability for the hybrid multirig with three-cycle-ad-tree toology as follows: R(G h-mr3c-t Pr[the multirig with three cycles are oeratioal] Pr[ edges i saig trees are oeratioal] We obtai (5 R(G h-mr3c-t ( ( ( ( ( 3 (6.. Hybrid Multirig with Commo-Node-ad-Tree I the hybrid multirig with commo-ode-ad-tree toology (G h-mrc-t (Figure g, the rigs are i the form of the mai rig coect with m sub-rigs ad other odes that are ot i the rigs form saig trees. Let i deotes the umber of odes i i th sub-rig, where deotes the umber of odes i the mai rig ad is the umber of edges i the saig trees. We derive the etwor reliability for the hybrid multirig with commo-ode-ad-tree toology as follows: R(G h-mrc-t Pr[the multirig with commo-ode are oeratioal] Pr[ edges i saig trees are oeratioal] We obtai R(G h-mrc-t 3. Prelimiary Results ad Discussio m i i { i ( } (7 i The relimiary umerical exerimets were coducted cosiderig a etwor cosistig of 6 odes ( 6. The robability of edge worig roerly,, is 0.9. We evaluate the etwor reliability of seve toologies as illustrated i Figure 3. I the multirig with three-cycle toology, the two sub-rigs cosists of odes i which 6 odes are i the commo ath searatig the mai rig ito two sub-rigs (i.e., c c 5, h 6. I the multirig with commo-ode toology, the mai rig cosists of four odes ad there are three sub-rigs; each cosists of four odes ( 3. I the hybrid sigle rig-ad-tree toology, there are four odes i the saig tree ad the remaiig odes are i the rig (i.e., m,. I the hybrid multirig with three-cycle-ad-tree toology, the mai rig cosists of odes ad the saig trees cosists of four odes (i.e., c c, h,. Lastly, i the hybrid multirig with commo-ode-ad-tree toology, the mai rig cosist of three odes ad there are three sub-rigs; each cosists of three odes ad the saig trees cosists of four odes (i.e., 3 3,. Table shows etwor reliabilities of those seve toologies. It aears that the saig tree toology has the lowest etwor reliability whereas the multirig with commo-ode toology has the highest oe. The reaso is Table. Networ reliability characteristics of differet toologies. NetworToology NetworCharacteristics Networ Reliability Saig Tree Saig tree of 6 odes Sigle Rig Sigle rig of 6 odes Multirig with three-cycle c c 5, h Multirig with commo-ode Hybrid sigle rig-ad-tree m, Hybrid multirig with three-cycle-ad-tree c c, h, Hybrid multirig with commo-ode-ad-tree 3 3, These toologies exist i ractical etwors ad are geerally used for the comariso i several studies (Ja 99; Charsriiyo et al., 00; Devaraj et al., 00; Billioet et al., 005.

5 C. Promma & E. Esoo / Soglaaari J. Sci. Techol. 3 (3, 63-69, that o bacu ath ca be formed i the saig tree toology i which a sigle li failure ca iterrut commuicatio services i the etwor whereas i the multirig with commo-ode toology, the bacu aths ca be formed i the multile rigs. It ca be observed that the sigle rig toology has the lowest etwor reliability comared to other forms of rig toologies. The etwor reliability of the multirig with threecycle toology is higher tha that of the sigle rig toology but lower tha that of the multirig with commo-ode toology. The reaso is that the sigle rig toology ca hadle oly a sigle li failure whereas the multirig toologies ca survive more tha oe li failure, give that oly oe li failure occurs i each sub-rig. The etwor reliabilities of the hybrid multirig-adtree toologies are much higher tha those of the saig tree ad the etwor reliabilities of the sigle rig toology are oly slightly lower tha those of the multirig toologies. Amog the etwor toologies cosidered i this examle, the etwor reliability of the hybrid multirig-ad-tree toologies is 6.78% ad 3.76% higher tha that of the saig tree ad the sigle rig toology, resectively, whereas it is oly about 37.73% less tha that of the multirig toologies. We ca see that the hybrid multirig-ad-tree toologies result i high etwor reliabilities ad they ca be alicable to the ractical etwors i case it may ot be ossible to istall commuicatio lis to form a rig of odes i some areas. Therefore, the hybrid toology is a alicable solutio, rovidig high etwor reliability ad relaxig the rig coectio reuiremets.. Coclusio I this aer, we roose etwor reliability aalysis of various etwors i terms of the oeratioal robability for 3G cellular toological etwor. We first showed the reliability aalysis for etwor toologies existig i curret etwors. Ad we the derived a ew etwor reliability models for the hybrid sigle rig-ad-tree ad the hybrid multirig-ad-tree toology. Next we showed the results of hybrid toology comarig with other toologies. which have higher reliability. We foud that the hybrid toologies result i high etwor reliabilities while relaxig the rig coectio reuiremets. Hece, the hybrid toology is a ovel solutio while there are limitatios i buildig the ractical etwors. Refereces Harmatos, J. 00. Plaig of UMTS core etwors. Proceedigs of the 3th Istitute of Electrical ad Electroics Egieers (IEEE Iteratioal Symosium o Persoal, Idoor ad Mobile Radio Commuicatios, Lisbo, Portugal, Setember 5-8, 00, Ja, R.-H. 99. Desig of reliable etwors. Proceedig of the IEEE Iteratioal Coferece o Commuicatios, Jue -8, 99, Charsriiyo, C. ad Wattaaogsaor, N. 00. A model for reliable wireless access etwor toology desig. Proceedig of the 0th IEEE Regio 0 Coferece, Chiag Mai, Thailad, November -, 00, Billioet, A., Elloumi, S. ad Grouz, L-D Desigig radio-mobile access etwors based o sychroous digital hierarchy rigs. Comuters & Oeratios Research. 3 (, Devaraj, D. ad Veeraumar, S. 00. Data commuicatio etwor desig usig geetic algorithm. Proceedigs of the IEEE Iteratioal Coferece o Itelliget Systems, Vare, Bulgaria, Jue -, 00, 6-66.

6 68 C. Promma & E. Esoo / Soglaaari J. Sci. Techol. 3 (3, 63-69, 00 Aedix The followig rovides derivatio of the etwor reliability for the saig tree, the sigle rig ad the multirig with three-cycle toology (Ja 99. Let G(V, E is a grah reresetig a etwor of odes V that are itercoected by a set of edges E. It is assume that all odes are erfectly reliable whereas the edges have oeratioal robability of (i.e. the robability of ot fuctioig of -. It is assumed that the failure of each edge occurs ideedetly. The etwor reliability of G is deoted by R(G, which is the robability that all odes i G ca commuicate with each other. Let V is the umber of odes i the etwor. - A saig tree toology (G st A saig tree is a toology cosistig of odes itercoected by - edges without formig ay loo (or rig. The etwor reliability of R(G st is writte as follows: R(G st Probability that - lis are i oeratioal state R(G st - A sigle rig toology (G r A sigle rig is a toology cosistig of odes itercoected by edges to form a rig cofiguratio. The etwor reliability of R(G r is writte as follows: R(G r Probability that lis are i oeratioal state + Probability that - lis are i oeratioal state R(G r C! (! - A multirig with three-cycle toology (G mr-3c A multirig with three-cycle is a toology i which the mai rig is searated ito two sub-rigs by a commo ath which is a series of coectig edges as show i Figure c. First, let us cosider a simle form of a multirig with three-cycle toology as show i Figure. It cosists of a rig of odes i which there is oe itercoected edge, called a commo edge, across the rig. We call this a sigle rig with a commo edge (G r+. The edge i-j is added i the toology so that the sigle rig is divided ito two arts; the first art cosistig of odes ad the secod art cosistig of odes where +. The etwor reliability of G r+ ca be derived as follows: R(G r+ Probability that all odes ca commuicate to each other while the i-j edge is i oeratioal state + Probability that all odes ca commuicate to each other while the i-j edge fails R ( G R( G ( R( r r G r { }{ } + { } { } + { } i G : j Figure. A sigle rig with a commo edge.

7 C. Promma & E. Esoo / Soglaaari J. Sci. Techol. 3 (3, 63-69, sice, Thus, R(G r+ To obtai the maximum etwor reliability, the fuctio R(G r+ is differetiated ad set to zero. The, it ca be derived that whe /, the etwor toology results i the highest etwor reliability. Now let us cosider the multirig with three-cycle toology (G mr-3c. The followig otatio is defied: the umber of edges i the commo ath h the umber of odes that are i the mai rig (i.e., ot i the commo ath For maximum etwor reliability, h/ Thus, the etwor reliability of the multirig with three-cycle toology, R(G mr-3c, ca be derived as follows: R(G mr-3c Probability that the odes i the first art ad the secod ath ca commuicate to each other while the commo ath is i oeratioal state + Probability that all odes i the mai rig ca commuicate to each other while the commo ath fails RG R G R Gh R( Gh R( Gh RGh h h h { h h } { h }{ } h h h h h h { h } { h }{ } h { } h h { { } {( [ } h h ( ( {( } ( ]}} ( ( 3 ( { } To obtai the maximum etwor reliability, the fuctio R(G mr-3c is differetiated ad set to zero. The, it ca be derived that whe (+/3, the etwor toology results i the highest etwor reliability. Substitutig i the euatio above we obtai R( G mr 3c ( (. 3