PROFIT EVALUATION OF A STOCHASTIC MODEL ON BASE TRANSCEIVER SYSTEM CONSIDERING SOFTWARE BASED HARDWARE FAILURES AND CONGESTION OF CALLS

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1 PROFIT EVALUATION OF A STOCHASTIC MODEL ON BASE TRANSCEIVER SYSTEM CONSIDERING SOFTWARE BASED HARDWARE FAILURES AND CONGESTION OF CALLS Rajeev Kumar and Sunny Kaoor Profeor, De of Maemaic, MD Univeriy Roak Reeaarc Scolar, De of Maemaic, MD Univeriy Roak ABSTRACT Te aer conider a ocaic model for a Bae Tranceiver Syem conidering four ye of failure viz. ardware, ofware, ofware baed ardware, caaroiailure and congeion of call. Variou faul in e yem are caegorized a minor or major faul(). I i aumed a e occurrence of a minor faul lead o arial failure werea a major faul and caaroiailure lead o comlee failure of e yem. On failure, e ecnician fir inec weer ere i ardware or ofware or ofware baed ardware failure en recovery of e relevan comonen i done. Uing Markov rocee and regeneraive oin ecniue variou meaure of yem erformance are obained. On e bai of ee meaure e rofi analyi of e yem i carried ou. Variou concluion abou reliabiliy and rofi of e yem are made on e bai of e graical udie Keyword: Bae Tranceiver Syem (BTS), caaroiailure, congeion of call, reliabiliy, rofi funcion, Markov roce, regeneraive oin ecniue.. INTRODUCTION A bae ranceiver yem (BTS) coni of bo ardware and ofware comonen a faciliae wirele communicaion beween uer euimen and a nework. Uer euimen are device like mobile one, WLL one, comuer wi Wi-Fi faciliy ec and e nework can be a of any wirele communicaion ecnologie like GSM, CDMA, Wi-Fi, WiMAX ec. Wen a BTS encouner failure eier due o ome ardware failure wic include volage anding wave raio(vswr) fail, AC failure, oical fiber cu, fan ray damage, double dulexer iming & managemen uni(dtmu), double dulexer ranmiing & receiving uni(dtru), double dulexer amlifier uni(datu), double dulexer ower uni(ddpu) fail ec. or ome ofware failure wic include faul in DTRU, DDPU, DATU, DTMU, ranor device ec. or ofware baed ardware failure like faul in DDPU, DTRU, DATU, DTMU, Tranor device ec. In a BTS ere may be caaroiailure like ower failure. In cae of occurrence of major faul, ere i comlee failure of yem werea in cae of occurrence of minor faul yem erformance and caaciy may decreae. Moreover wen ere i auraion or congeion of call in BTS en e ervice for ome ubcriber of nework i reduced or call are unaended. A BTS uor e air inerface connecion wi mobile o e reliabiliy and availabiliy lay a very ignifican role in mobile yem and ence need o be analyzed. In e field of reliabiliy modeling everal reearcer Gua and Kumar (983), Rizwan and Taneja (000), Kumar e al (00), Kumar and Baia (0) analyzed a large number of yem conidering variou conce uc a differen failure mode, mainenance, reair, relacemen, inecion, oeraional age ec. For ardware-ofware yem, Teng e al (006), Tumar and Smid (0), Welke e al (995) dicued variou ye of ardware and ofware failure. Recenly Kumar and Kaoor (0) carried ou e co-benefi analyi of reliabiliy model for a Bae Tranceiver Syem conidering ardware/ ofware faul and congeion of call. However none of e reearcer a carried ou e analyi of BTS conidering e ofware baed ardware failure and caaroiailure. Keeing i in view, e reen aer analye a one uni BTS yem aving ardware, ofware, ofware baed ardware and caaroiailure including congeion of call. Variou faul in e yem are caegorized a minor faul and major faul. Variou minor faul include VSWR fail, DTRU fail, DDPU fail, fan ray damage ec werea Volume, Iue 3, Marc 03 Page 554

2 major faul include AC failure, ranor device fail, oical fiber cu, DTMU fail ec. I i aumed a e occurrence of a minor faul lead o arial failure werea a major faul and caaroiailure lead o comlee failure of e yem. On failure, e ecnician fir inec weer ere i ardware or ofware or ofware baed ardware failure en recovery of e relevan comonen i done. For analyi uroe e daa ued ere i colleced from Vodafone Sace Tel Ld, Biar and variou Failure/reair/relacemen rae and robabiliie comued from e daa a given below: Rae of occurrence of major faul =.007 Rae of occurrence of minor faul =.003 Rae of occurrence of ofware baed major ardware faul = Rae of occurrence of ofware baed minor ardware faul = Probabiliy a e major ardware faul occur in e yem =.7 Probabiliy a e major ofware faul occur in e yem =.7 Probabiliy a e caaroiaul occur in e yem =. Probabiliy a e minor ardware faul occur in e yem =.75 Probabiliy a e minor ofware faul occur in e yem =.5 Reair rae on occurrence of major ardware faul =.54 Reair rae on occurrence of major ofware faul =.57 Reair rae on occurrence of minor ardware faul =.98 Reair rae on occurrence of minor ofware faul =.83 Relacemen rae on occurrence of ofware baed major ardware faul =.84 Relacemen rae on occurrence of ofware baed minor ardware faul =.8 Relacemen rae on occurrence of caaroiaul =.60 Uing Markov rocee and regeneraive oin ecniue variou meaure of yem erformance are obained. On e bai of ee meaure and eimaed arameer e rofi analyi of e yem i carried ou. Variou concluion abou reliabiliy and rofi of e yem are made on e bai of e graical udie. NOTATIONS λ / λ λ 3 / λ 4 Rae of occurrence of major/minor faul Rae of occurrence of ofware baed major/minor ardware faul Rae of congeion of call α Rae wi wic yem reored afer congeion a / a Probabiliy a e major/minor ardware faul occur in e yem b / b r Probabiliy a e major/minor ofware faul occur in e yem c Probabiliy a e caaroiaul occur in e yem ij / Q ij Probabiliy of raniion from ae i o ae j g / g P.d.f. of reair ime of major/minor ardware faul g / g. P.d.f. of reair ime of major/minor ofware faul / P.d.f. of relacemen ime of ofware baed major/minor ardware faul 3 4 P.d.f. of relacemen ime of caaroiaul i / i P.d.f. of inecion ime of major/minor faul I / I C.d.f. of inecion ime of major/minor faul G / G C.d.f. of reair ime of major/minor ardware faul G / G 3 4 C.d.f. of reair ime of major/minor ofware faul H / H C.d.f. of relacemen ime of ofware baed major/minor ardware faul Volume, Iue 3, Marc 03 Page 555

3 H P.d.f. of relacemen ime of caaroiaul O O c O i / F i Oeraive ae Congeion ae Down ae/failed ae under inecion O / O Down ae due o ardware/ofware faul under reair r r r O / F Down ae/failed ae due o ofware baed ardware faul under relacemen F / F r r r Failed ae due o ardware/ofware faul under reair F cf r Failed ae due o caaroiaul under relacemen OTHER ASSUMPTIONS. A minor or major faul may be in a ardware or ofware comonen.. Te yem auomaically reore from e congeion of call. 3. Te ecnician immediaely andle all ye of faul a BTS ie. 4. Rae of occurrence of faul, congeion and yem reoraion are conan werea reair and inecion ime diribuion are arbirary. 5. Afer eac reair/relacemen e yem i a good a new. 6. Swicing i erfec and inananeou. 7. All random variable are muually indeenden. THE MODEL A diagram given in figure ow variou ae of raniion of e yem. Te decriion abou e noaion ued and e ae of e yem are given in e Aendix. Te eoc of enry in o ae 0,,,3,4,5,6,7,8,9,0 are regeneraive oin, i.e. all e ae are regeneraive ae. Oeraive Sae Failed Sae Down Sae Congeion Sae Figure Sae Traniion Diagram Volume, Iue 3, Marc 03 Page 556

4 . TRANSITION PROBABILITIES AND MEAN SOJOURN TIMES Le Q ij be e cumulaive diribuion funcion (c.d.f.) of fir aage ime from a regeneraive ae i o a regeneraive ae j or o a failed ae j wiou viiing any oer regeneraive ae in (0, ] en variou raniion robabiliie are given by e following euaion: ( ) e ( ( ) e ) ( ( ) e ) 0 4 ( ) a i ( ) 0 5 ( ) b i ( ) 6 03 ( ) c i ( ) 7 ( ) a i ( ) 8 ( ) b i ( ) e 30 ( ) 40 g e g 59 3 e G g 4 80 e g e G 00 4 Te non-zero elemen ij lim () 0 ij bi (0) 6 ci (0) 7 8 b i (0) g ( 3 ) c f 70 g (0) (0) 3 00 (0) 4 a i (0) a i (0) g (0) (0) g ( ) g ( ) g ( ) By ee raniion robabiliie, i can be verified a = = = = = 30 = 40 = 60 = 70 = 90 = 00 = Te mean ojourn ime (µ i ) in e regeneraive ae i i defined a e ime of ay in a ae before raniion o any oer ae, en i (0) 0 i (0) 3 4 g (0) ( g ( )) cf (0) 7 g (0) ( g ( )) (0) 0 4 (0) Te uncondiional mean ime aken by e yem o rani for any regeneraive ae j, wen i i couned from eoc of enrance ino a ae i, i maemaically aed a m ij ijd 0 Tu, m 0 + m 0 + m 03 = 0 m 4 + m 5 +m 6 = m 7 + m 8 = m 30 = 3 m 40 = 4 m 50 +m 59 = 5 m 60 = 6 m 70 = 7 m 80 +m 80 = 8 m 90 = 9 m 00 = 0 MEAN TIME TO SYSTEM FAILURE To deermine e MTSF of e yem, e failed ae of e yem are aken a aborbing ae. By robabiliic argumen, Te following recurive relaion for i, c.d.f of e fir aage ime from regeneraive ae i o failed ae, are obained: 0 =Q 0 + Q 0 + Q 03 3 Volume, Iue 3, Marc 03 Page 557

5 = Q Q = Q = Q = Q Q = Q 00 0 Uing Lalace Sielje ranform, e above recurive relaion are olved in erm of () 0 Te mean ime o yem failure (MTSF) wen e yem ar from e ae 0,i were 0 () N T0 lim, 0 D N = µ µ + 03 µ ( 7 µ µ µ 0 ) D= OTHER MEASURES OF SYSTEM PERFORMANCE Uing robabiliic argumen for regeneraive rocee, variou recurive relaion are obained and are olved o derive imoran meaure of e yem erformance. Toe are a given below: were Execed u ime of e yem (A 0 ) = N / D Execed down ime of e yem (DT 0 ) = N / D Execed congeion ime of e yem (CT 0 ) = N 3 / D Buy eriod of reair man (Inecion ime only) (B i ) = N 4 / D Buy eriod of reair man (Reair ime only) ( BR 0 ) = N 5 / D Buy eriod of reair man (Relacemen ime only) (BRP 0 ) = N 6 / D N = μ 0 N = 0 µ µ µ µ 0 N 3 = 03 µ 3 N 4 = 0 µ + 0 µ N 5 = 0 4 µ µ µ µ 8 N 6 = µ µ µ 6 D = µ µ + 0 µ + 03 µ µ µ µ µ µ µ µ 0 3. PROFIT ANALYSIS Te execed rofi incurred of e yem i given by P = C 0 A 0 C DT 0 C CT 0 C 3 BI 0 C 4 BR 0 -C 5 BRP 0 -C were C 0 = revenue er uni uime of e yem C = co er uni downime of e yem C = co er uni congeion ime of e yem C 3 = co er uni ime of inecion C 4 = co er uni ime of reair C 5 = co er uni ime of relacemen C = co of inallaion of e yem 4. GRAPHICAL ANALYSIS For graical analyi e following aricular cae are conidered: Volume, Iue 3, Marc 03 Page 558

6 g e i ( ) e g e i e e cf cf g e e g e 4 4 e 4 Variou gra for meaure of yem erformance viz. MTSF and rofi are loed for differen value of rae of occurrence of faul (λ, λ, λ 3, λ 4 ),robabiliie of occurrence of ardware/ofware/caaroiaul (a, b, a, b, c ), inecion rae (, ), ardware/ofware reair rae (,,, ),relacemen rae (, 3, 4 ),call congeion and yem reoraion rae (η, α). Fig. give e gra beween MTSF (T 0 ) and rae of occurrence of major faul (λ ) for differen value of rae of occurrence of ofware baed minor ardware faul (λ 4 ). Te gra reveal a MTSF decreae wi increae in e value of e rae of occurrence of major faul. Furer i can be oberved a MTSF decreae wi e increae in e value of rae of occurrence of ofware baed minor ardware faul. Figure. Fig. Te gra in figure 3 ow e aern of rofi wi reec o e rae of occurrence of minor faul (λ ) for differen value of rae of occurrence of major faul (λ ). Te curve in e gra indicae a e rofi of e yem decreae wi e increae in e value of e rae of occurrence of minor a well a major faul. Furer from e gra i may alo be noiced a for λ = 0.00 e rofi i > or = or < 0 according a λ i < or = or > Hence e yem i rofiable o e comany wenever λ Similarly, for λ = 0.08 and λ = 0.6, e rofi i > or = or < 0 according a λ i < or = or > and 0.09, reecively. Hence in ee cae e yem i rofiable o e comany wenever λ and 0.09 reecively. Figure 3 Te gra in figure 4 ow e aern of rofi wi reec o e rae of occurrence of major faul (λ ) for differen value of rae of occurrence of ofware baed major ardware faul (λ 3 ). Te curve in e gra indicae a e rofi of e yem decreae wi e increae in e value of e rae of occurrence of major a well a ofware baed major ardware faul. Furer from e gra i may alo be noiced a for λ 3 = e rofi i > or = or < 0 according a λ i < or = or > Hence e yem i rofiable o e comany wenever λ Similarly, for λ 3 = and λ 3 = 0.006, e rofi i > or = or < 0 according a λ i < or = or > 0.85 and 0.3, reecively. Hence in ee cae e yem i rofiable o e comany wenever λ 0.85 and 0.3 reecively. Volume, Iue 3, Marc 03 Page 559

7 Fig. 4 Figure 4 Te gra in figure 5 ow e aern of rofi wi reec o e rae of occurrence of minor faul (λ ) for differen value of rae of occurrence of ofware baed minor ardware faul (λ 4 ). Te curve in e gra indicae a e rofi of e yem decreae wi e increae in e value of e rae of occurrence of minor a well a ofware baed minor ardware faul. Furer from e gra i may alo be noiced a for λ 4 = e rofi i > or = or < 0 according a λ i < or = or > 0.0. Hence e yem i rofiable o e comany wenever λ 0.0. Similarly, for λ 4 = and λ 4 = , e rofi i > or = or < 0 according a λ i < or = or > 0.4 and 0.078, reecively. Hence in ee cae e yem i rofiable o e comany wenever λ 0.4 and reecively. Figure. 5 Te gra in figure 6 ow e aern of rofi wi reec o e rae of occurrence of congeion of call (η) for differen value of co er uni congeion ime of e yem (C ). Te curve in e gra indicae a e rofi of e yem decreae wi e increae in e value of e rae of occurrence of congeion of call a well a wi co er uni congeion ime of e yem. Furer from e gra i may alo be noiced a for C = 80 e rofi i > or = or < 0 according a η i < or = or > Hence e yem i rofiable o e comany wenever η Similarly, for C = 480 and C = 680, e rofi i > or = or < 0 according a η i < or = or >.56 and 0.46, reecively. Hence in ee cae e yem i rofiable o e comany wenever η 0.56 and 0.46 reecively. Figure. 6 Volume, Iue 3, Marc 03 Page 560

8 Te curve in e figure7 ow e beavior of e rofi wi reec o e revenue er uni u ime (C 0 ) of e Fig. yem 6 for e differen value of rae of ofware baed major ardware faul (λ 3 ). I i eviden from e gra a rofi increae wi e increae in e value of revenue er uni u ime of e yem for a fixed value of e rae of occurrence of ofware baed major ardware faul. From e fig. 7 i may alo be oberved a for λ 3 = , e rofi i > or = or < 0 according a C 0 i > or = or < R Hence e yem i rofiable o e comany wenever C 0 R Similarly, for λ 3 = and λ 3 = e rofi i > or = or < 0 according a C 0 i > or = or < R and R reecively. Tu, in ee cae, e yem i rofiable o e comany wenever C 0 R and R reecively. Figure 7 5. CONCLUSION AND DISCUSSION From e gra i i concluded a e mean ime o yem failure of e BTS deceae wi e increae in e value of e rae of occurrence of major a well minor ardware, ofware and ofware baed ardware faul. Furer i may alo be oberved a rofi of e yem decreae wi increae in e rae of occurrence of major and minor faul. I alo decreae wi increae in e rae of occurrence of ofware baed ardware faul. Te rofi of e yem alo decreae wi increae in congeion rae and co er uni congeion ime of e yem bu increae wi e increae in e revenue er uni uime of e yem. Variou cuoff oin for revenue er uni uime, rae of occurrence of major and minor faul can be obained. Alo for fixed value of co er uni congeion ime of e yem, cuoff oin for rae of occurrence of congeion can be obained. REFERENCES [] Goalan, M.N. and Banu, K.S. (995) Co analyi of wo-uni reairable yem ubjec o online revenive mainenance and/or reair Microelecron Reliabiliy, 35(), [] Gua, M.L. and Kumar, A. (983) On rofi conideraion of a mainenance yem wi minor reair, Microelecron Reliabiliy, 3, [3] Kumar, R. and Baia, P. (0) Reliabiliy and co analyi of one uni cenrifuge yem ingle reairman and inecion, Pure and Alied Maemaika Science, 74 (-), 3-. [4] Kumar, R., Kaoor, S.(0) Co-benefi analyi of reliabiliy model for a bae ranceiver yem conidering ardware/ ofware faul and congeion of call, Inernaional Journal of Advance in Science and Tecnology, Secial Iue, 3-3. [5] Kumar, R., Mor, S.S. and Sarma, M.K.(00) Reliabiliy and co benefi analyi of a ree age oeraional warraned oiicaed yem wi variou minor and major faul, Pure and Alied Maemaika Science, 7,9-38. [6] Murari, K. and Goyal, V. (983) Reliabiliy yem wi wo ye of reair faciliie, Microelecron Reliabiliy, 3(6), [7] Rizwan, S.M. and Taneja, G.(000) Profi analyi of yem wi erfec reair a arial failure or comlee failure, Pure Alied Maemaika Science,LII(-),7-4. [8] Teng, X., Pam, H. and Jeke, D.R. (006) Reliabiliy modeling of ardware and ofware ineracion, and i alicaion, IEEE Tranacion on Reliabiliy, Vol. 55, No. 4, [9] Tumer, I.Y. and Smid, C.S. (0) Inegraed deign-age failure analyi of ofware driven ardware yem,ieee Tran on Comuer, Vol 60, No.8, Volume, Iue 3, Marc 03 Page 56

9 [0] Tueja, R.K., Arora, R.T. and Taneja, G. (99) Analyi of wo-uni yem wi arial failure and ree ye of reair Reliabiliy Engineering and Syem Safey, 33, [] Welke, S.R., Jonon, B.W. and Aylor, J.H.(995) Reliabiliy modeling of ardware/ofware yem, IEEE Tran of Reliabiliy, Vol 44, No.3, AUTHORS PROFILE Dr Rajeev Kumar i currenly working a Profeor in e Dearmen of Maemaic, M.D. Univeriy, Roak. He a a eacing exerience of abou 4 year a variou iniuion like Punjab Univeriy, Candigar and M.D. Univeriy, Roak for wide range of UG/PG level coure. He a a reearc exerience of abou 4 year in e area of Reliabiliy Engineering, Oeraion Reearc and Saiical Eimaion. He a done i M.Sc. and P.D. from M.D. Univeriy Roak, M.Pil from C.C.S. Univeriy, Meeru and PGDCA, from IGNOU, New Deli. He i a life member of variou academic/reearc ocieie/bodie. He a ariciaed in around 30 Naional/ Inernaional ymoia/conference. Sunny Kaoor received er M.Sc. in Maemaic (Gold Medal) from MD Univeriy Roak in 004 and M.Pil. in Alied Maemairom Kurukera Univeriy, Kurkera in 007.Currenly e i doing reearc in e area of Reliabiliy Engineering. Volume, Iue 3, Marc 03 Page 56