Journal of Global Research in Computer Science A MARKOV CHAIN MODEL FOR ROUND ROBIN SCHEDULING IN OPERATING SYSTEM

Transcription

1 Volue 2, No 6, June 20 Journal of Global Research n Coputer Scence RESEARCH AER Avalable Onlne at wwwjgrcsnfo A MARKOV CHAIN MODEL FOR ROUND ROBIN SCHEDULING IN OERATING SYSTEM Deepak Ssoda *, Dr Sohan Garg 2 Assstant rofessor, Departent of Coputer Scence, SV Unversty of Agrculture & Technology, Meerut (U) deepakssoda02@galco 2 Assocate rofessor, Departent MCA, RKGIT, 5 th KM Stone, Delh-Meerut Road, GZB (U) sohangarg@redffalco Abstract: In the Round-Robn schedulng schee, the scheduler processes each job, one after another, after gvng a preset quantu of te In the frst-n frst out (FIFO) schedulng, next process gets the opportunty only f the earler arrved job s copletely processed Ths paper presents a general class of round-robn schedulng schee n whch both the above schedulng procedures are covered lke partcular cases Ths class has any other schedulng schees also A Markov chan odel s used to copare several schedulng schees of the class One schedulng schee, whch s a xture of FIFO and round robn, s found effcent n ters of odel based study approach The syste sulaton procedure s used to derve the concluson of the content INTRODUCTION In an operatng syste, a large nuber of processes arrve to the scheduler whose role s to anage the processng of these jobs There are any schedulng schees avalable n lterature [see Slberschatz and Galvn (2007), Stallng (2004), Tanenbau and woodhull (2007)] lke FIFO, Round robn, rorty based, Mult-level queue schedulng and so on All these schees have soe advantages and dsadvantages over each other A unfed study of schedulng schee s requred under a coon envronent of the syste Ths otvates to desgn unfed a general class of schedulng schees contanng well known schees so that ts ebers ay possess coon propertes of the class as well as could be utually copared Wth ths thought of otvaton, a general class of schedulng schee s desgned n ths paper contanng soe well-known schees lke FIFO and Round robn as ts eber schees Shukla and Jan (2007) have studed the ult-level queueschedulng schee n the envronent of Markov chan odel Shukla etal (2007), studed the setup of space dvson swtches n a Markov chan odel scenaro Shukla and Jan (2007) used a Markov chan odel for deadlockbased study of ult-level queue schedulng Soe other contrbutons related to the use of Markov chan odel are due to Medh (99) and Nald (2002) and to round robn, queung syste are due to Schassberger (98), Eserberg (979), Lu and Towsley (994), Chang (994), Nelson and Towsley (994), Shenker and Wenrb (989), Nelson, Towsley and Tantaw (988) and Horn (974) In present study, the desgned general class of schedulng schee s exaned through a Markov chan odel n order to perfor coparatve analyss of perforance of eber schedulng schees GENERAL CLASS OF ROUND-ROBIN QUEUE SCHEDULING SCHEME Consder a round-robn schedulng schee shown n fg 2 A general class s lad down below: A) the S denotes scheduler and there are processes, 2, 3, n queue; B) the S provdes one quantu of te to each process and next quantu s decded by a rando tral; C) the S starts fro any process n queue and then oves to j ( j =,2,3 ) ; D) The new process enters fro the end e + s placed after and so on; E) Suppose S s at any process (,2,3 ) at the end of a quantu, then n the next quantu (a) S wll be on + wth prorty p, or (b) S wll be on wth prorty s, or (c) S wll be on - wth prorty q F) The S becoes dle when there s no process n the queue However t s assued that the scheduler S ay be n deadlock state n any quantu; G) Fro ths deadlock level, the S could be back also to the queue n any other quantu for processng purpose; H) There s a long watng queue of processes, 2 outsde the processng unt and f one process s over nsde, then a new process, watng outsde, enters nsde so as to antan the length of processes there JGRCS 200, All Rghts Reserved

2 Deepak Ssoda et al, Journal of Global Research n Coputer Scence Volue 2 Issue (6), June 20 Fgure (Round Robn rocessng) 3 2 MARKOV CHAIN MODEL ( ) Let { X n, n } denotes a Markov chan wth the state space, 2, 3, and D where D s a deadlock state used to denote dle level, blockng or any dsturbance caused n the syste, durng job processng The X s the state th of scheduler of the syste at the end of n quantu (n=,2,3 ) Assue that processes are n syste at a te Further, let the transton of scheduler S s rando th over + states n n quantu The transton dagra for any three processes -,, + and D s gven n fg 3 Fgure2 (Syste Dagra Defne unt-step transton probabltes as [X (n+) = + /X (n) = ] = p [X (n+) = /X (n) = ] = s [X (n+) = - /X (n) = ] = q [X (n+) =D /X (n) = ] = r [X (n+) = /X (n) =D] = 0 The unt step transton probablty atrx s: wth p + q + r + s = and (+)r = The ntal probabltes, at n=0 for general class are : [X (0) = ] = pb (,2,3,4 ) [X (0) =D] = 0 The state probabltes after the frst quantu [X () = ] = [X (0) = - ] [X () = / [X (0) = - ] + [X (0) = ] [X () = / [X (0) = ] + [X (0) = + ] [X () = / [X (0) = + ] = (pb - )p + (pb )s + (pb + )q (f -=0 then -= & f +> then +=) [X () =D] = r pb = r Slarly, state probabltes after second quantu can be obtaned by sple relatonshp: [X (2) = ] = [(pb -2 )p + (pb - )s + (pb )q]p+ [(pb - )p + (pb )s + (pb + )q]s+ [(pb )p + (pb + )s + (pb +2 )q]q+ r0 = [X () = - ]p+ [X () = ]s+ [X () = + ]q [X (2) ( ) ( ) =D] = [ X = ] r + [ X D] = In the slar way, state probabltes after thrd quantu [X (3) = ] = [X (2) = - ]p+ [X (2) = ]s+ [X (2) = + ]q [X 3) =D] = n ( 2) ( 2) [ X = ] r + X [ D] = Reark 3 The generalzed expressons for n quantu could be expressed lke: [X (n) = ] = [X (n-) = - ]p+ [X (n-) = ]s+ [X (n- ) = + ]q n [X (n) ( n ) ( n ) =D] = [ X = ] r + [ X = D] SOME SECIAL SCHEDULING SCHEMES By posng restrctons and condtons over the ways and procedures, one can generate varous schedulng schees fro the generalzed class n secton 20 SCHEME- III [A]: WHEN Q = 0, R=0, + S= Unt step transton probablty atrx for schee-iii [A] s X under JGRCS 200, All Rghts Reserved 2

3 Deepak Ssoda et al, Journal of Global Research n Coputer Scence Volue 2 Issue (6), June 20 [X (0) = ]=pb [X (0) =R ]=0 (,2,3 ) Reark The ntal probabltes at n=0 for schee-iii [A] [X (0) = ]=pb and subject to the condton pb Reark2 The state probabltes after the frst quantu [X () = ]=pb - p + pb s Reark 3 The state probabltes after the second quantu [X (2) = ]=[X () = - ]p + [X () = ]s Reark 4 The generalzed expressons of schee-iii [A] for n quantu [X (n) = ]= [X (n-) = - ]p + [X (n-) = ]s SCHEME- III [B]: WHEN q = 0, p + r + s = Unt step transton probablty atrx for schee-iii [B] s X under and subject to the condton pb Reark2 The state probabltes after the frst quantu [X () = ]= [X (0) = - ]p + [X (0) = ]s [X () =R ]= r pb = r Reark3 The state probabltes after the second quantu [X (2) = ]=[X () = - ]p + [X () = ]s [X (2) ( ) =D ]= [ X = ] Reark4 The generalzed expressons of schee-iii [B] for n quantu [X (n) = ]=[X (n-) = - ]p + [X (n-) = ]s [X (n) =D ]= SIMULATION STUDY ( n ) [ X = ] In order to copare all the four schedulng schees wth parts theren, under a coon setup of Markov chan odel, the followng sulaton study s perfored: Under Schee-III [A]: Consder ntal probabltes pb =027, pb 2 =05, pb 3 =07, pb 4 =08, pb 5 =023 and the transton probablty atrx lke below: {Here s=05, p=05, q=r=0 and p + s = } Reark The ntal probabltes at n=0 for schee-iii [B] are Table X = p for transton probablty atrces Quantu [ ] ) SC III ( A robabltes n = n = n = n = n = JGRCS 200, All Rghts Reserved 3

4 Deepak Ssoda et al, Journal of Global Research n Coputer Scence Volue 2 Issue (6), June 20 n = n = p p p3 p4 p5 Fgure3 Fgure4 The schee-iii [A] shown n fg 55[A] and 55[B] s nether FIFO nor a round robn schee But t s a xture of these two In ths, the quantu dstrbuton takes over the sae state or to the next state dependng upon the outcoe of the rando experent If the nuber of quantu ncreases then ths schee shows alost a stable pattern of the state probabltes Ths eans every process has alost sae chance of beng processed Under Schee-III [B]: Intal probabltes are pb =027, pb 2 =05, pb 3 =07, pb 4 =08, pb 5 =023, pb r =0 and the transton probablty atrx lke below: {Here q = 0, p + r +s = and r = 066} Table2 [ X = p ] for transton robablty Matrces ) SC III (B Quantu robabltes D n = n = n = n = n = n = n = Fgure5 and Fgure6 When III [B] s taken nto consderaton, whch s wth deadlock chances also, we found that wth the ncreasng nuber of attepts, the state probabltes are reducng and there s a hgh chances of syste beng transferred to deadlock state Fg f6[a] and 56[B] are n support of these facts JGRCS 200, All Rghts Reserved 4

5 Deepak Ssoda et al, Journal of Global Research n Coputer Scence Volue 2 Issue (6), June 20 CONCLUDING REMARK The present study ncorporates a general class of schedulng schees wth FIFO and round robn as ts ebers Soe other schees are also eber of ths class and all these are consdered wth and wthout deadlock state All the schees are studed under a coon Markov chan odel If the nuber of quantu ncreases then schee-iii[a] shows alost a stable pattern of state probabltes The schee-iii sees a good choce because of stablty pattern over job processng REFERENCES [] Chang, CW (994): Stablty, queue length and delay of deternstc and stochastc queung network, IEEE Transactons of Autoatc control, Vol 39, pp [2] Esenberg, M (979): Two queues wth alternatve servce, SIAM Journal of appled atheatcs, Vol 36,pp [3] Horn, W (974): Soe sple schedulng algorths, Naval Research Logstc Quaterly, Vol 2, pp [4] Lu, Z and Towsley, D (994): Optalty of the round robn routng polcy, Journal of appled probablty, Vol 26(), [5] Medh, J (99): Stochastc processes, Ed 4, Wley Lted (Fourth Reprnt), New Delh [6] Nald, M (2002): Internet access traffc sharng n a ult-user envronent, Coputer Networks, Vol 38, pp [7] Nelson, R and Towlsey, D (993): A perforance evaluaton of several prorty polces for parallel processng systes, Journal of ACM, Vol 40, pp [8] Nelson, R, Towlsey, D and Tantaw, AN (988): erforance analyss of parallel processng syste, IEEE Transacton of Software Engneerng, Vol 4, pp [9] Schassberger, R (98): On the response te dstrbuton n a dscrete round robn queue, Acta Infoatca, Vol 6 (), pp [0] Shenker, G and Wenrb, A (989): The optal control of heterogeneous queung systes, A paradg for load sharng and routng, IEEE Transacton of Coputers, Vol 38, pp [] Shukla, D and Jan, Saurabh (2007): A Markov chan odel for ult-level queue scheduler n operatng syste, roceedngs of the Internatonal Conference on Matheatcs and Coputer Scence, ICMCS-07, pp [2] Shukla, D and Jan, Saurabh (2007): Deadlock state study n securty based ult-level queue schedulng schee n operatng syste, roceedngs of Natonal Conference on Network Securty and Manageent, NCNSM-07, pp [3] Shukla, D Gadewar, S athak, RK (2007): A Stochastc odel for space-dvson swtches n coputer networks, Appled atheatcs and Coputaton (Elsever Journal), Vol 84, Issue 2, pp [4] Slberschatz, A, Galvn, (999): Operatng syste concept, Ed5, John Wley and Sons (Asa), Inc [5] Stallng, W (2004): Operatng systes, Ed5, earson Eduacton,Sngopore,Indan Edton, New Delh [6] Tanenbau, A and Woodhull, AS (2000): Operatng syste, Ed 8, rentce Hall of Inda, New Delh JGRCS 200, All Rghts Reserved 5