A multichannel Satellite Scheduling Algorithm

Transcription

1 A multichannel Satellite Scheduling Algoithm J.S. Gilmoe and R. Wolhute Depatment of Electonic Engineeing Univesity of Stellenbosch 7600 Stellenbosch, South Afica Abstact Duing the design pocess of the South Afican Sumbandilasat satellite, a equiement was identified fo a stoeand-fowad type on-boad communications payload. This will allow fo connectivity with emote ual gound stations. Due to othe systems design constaints, these communications wee limited to a single, half-duplex channel with 9600 baud capacity. This expeience highlighted the equiement fo a multichannel payload, to cate fo the ising need fo highe bandwidth data tansfe to- and fom emote pats of Afica. To this effect, a new payload is being designed fo a next geneation satellite, offeing a total of 23, 9600 baud communication channels, allowing multiple, simultaneous stoe-and-fowad connections to gound stations. Due to the possible excess of gound stations ove available channels, a scheduling poblem occus. This pape pesents a scheduling algoithm to do satellite on-boad scheduling fo the gound station links. The aim of the algoithm is to schedule all gound stations in the available communication time window as faily as possible and in accodance with individual gound station equiements. I. INTRODUCTION Some pevious multi-channel satellites only acted as tansmittes, whee data could not flow fom a gound station to the eceive. Gound stations would only tune to the specific channel s tansmission fequency and eceive the date tansmitted [1]. This is used fo boadcasts, whee many eceiving gound stations exist, but only one tansmitting gound station. No pevious multi-channel communication satellites ae known to have been developed in Afica. What makes the Afican context diffeent fom othe pats of the wold, is how isolated some egions of the county ae. When thee ae many gound stations communicating with a satellite, these gound stations have to be scheduled. This pape eseaches a scheduling scheme by which all gound stations that connect, ae allowed to communicate befoe the satellite passes out of communications ange. The satellite system is chaacteised to obtain the un-time paametes and bounday values of the system. A simulato is designed to simulate the satellite-gound station model. Scheduling algoithms ae fomulated and investigated in the simulato to benchmak thei pefomance against some basic scheduling algoithm. These algoithms ae compaed to discove which algoithm pefoms the best. Section II descibes the details of the position and velocity of the satellite, and how these chaacteistics may be used to compute the gound station acquisition ate of the satellite. Section III defines the multichannel satellite scheduling poblem in scheduling tems. Section IV descibes the simulation model used to evaluate the scheduling algoithms on. Section V Fig. 1. h l d Eath Diagam of satellite obit popeties θ s v Satellite descibes a basic scheduling algoithm that may be used to solve the satellite scheduling poblem and then goes on to descibe possible impovements to this algoithm. Section VI pesents the esults of the simulations and compaes the diffeent scheduling algoithms. Section VII descibes what wok has been done in this pape and povides some futue impovements that will be made. II. SATELLITE SYSTEM CHARACTERISTICS The satellite is in a pola sun-synchonous obit [2] at a height of h = 500 km above sealevel. Such an obit ensues that a satellite will pass though a cetain hoizontal line at appoximately the same local time fo each cossing. A satellite might pass ove the equato twelve times a day, each time passing the equato at aound 12:00, local time. The sunsynchonous obit of the satellite ensues that the satellite tavels ove South-Afica at aound the same time each day. The satellite completes one eath otation in 100 min. The aveage adius of the eath is taken as = 6371 km [3]. Figue 1 shows a diagam of the satellite obiting the Eath. Fom these values, the appoximate velocity of the satellite may be calculated. If the eath is assumed to be cicula, the distance the satellite tavels in a day is given by the fomula fo the cicumfeence of a cicle: p = 2π ( + h) (1) = 2π ( ) = km Equation (1) gives the path length (p) of the satellite. The velocity of the satellite (v) may now be calculated using

2 equation (2). v = p (2) t km = = km/h 100 min Next, the velocity of the satellite s footpint, tavelling along the eath s suface, can be calculated. This is done by pojecting the satellite s velocity down to the suface of the eath. Fom figue 1, it can be seen that the ac the satellite makes when tavelling though space, is subtended by an ac on the suface of the eath. The velocity of the satellite s footpint is then given by: s = v d (3) l Equation (3) gives the footpint s velocity (s) as the satellite s velocity (v), scaled by the lengths of the acs l and d. Again looking at figue 1, fom geomety: θ = d = l + h theefoe, d l = + h Substituting equation (4) into equation (3): s = v + h ( ) 6371 = = km/h Equation (5) gives s in tems of v and the height of the satellite above the eath, whee the adius of the eath is taken to be constant. This shows that the velocity of the satellite s footpint is not dependend on the length of the path it tavels, which is to be expected. It also shows that the velocity of the satellite s footpint is not much smalle than that of the satellite itself. The eason fo this is the low altitude of the satellite compaed to the adius of the eath. Using s, the gound station acquisition time (t aq ) may be calculated with t aq = d RSA s 1000 km = 2,5 min km/h Equation (6) gives the time which the satellite s footpint will take to tavel d RSA = 1000 km. This is appoximately the length the footpint will tavel acoss South Afica. The satellite-gound station negotiation time can be calculated using equation (7). t x,min = h (7) c = 500 = 1,67 ms whee t x,min gives the minimum tavel time of a packet between the satellite, and a gound station diectly below the satellite, and c is the speed of light in a vacuum. Satellite-gound station communications ae line-of-site, i.e. the distance fom the satellite to a gound station may be moe that 500 km. Next (4) (5) (6) Fig. 2. Gound station lmax φ Eath Diagam depicting the line of site paametes h Satellite we calculate the maximum distance the satellite can be fom a gound station. Figue 2 shows the point at which a gound station will be able to initiate communications with the satellite. This is whee the satellite intecepts the hoizontal line, dawn fom a gound station on the Eath s suface. This line is tangential to the cicle. If this line is tilted, it will intecept the cicle a second time, showing that thee is no line-of-site to an object below the tangential line. The ealiest point whee thee may be communication, is whee the satellite intecepts the tangential line. Equation (8) now gives the angle φ, using tigonomety. = cos φ (8) + h = cos φ φ = 21,99 = 0,3838 ad Using the maximum communications ange (δ max ) obtained fom equation (9), the maximum packet tavel time (t x,max ), can now be calculated using equation (10). δ max = tan φ = 2573 km (9) t x,max = δ max c = 8,58 ms (10) The maximum ound-tip-time (RTT) is then RTT = 2 t x,max = 17,16 ms. The communication time window length (T C ), is the length of time that a gound station is in line of site contact with the satellite. To obtain this, the length the satellite tavels though space in visible ange of the gound station is used. This distance, combined with the velocity of the satellite gives T C. l C = ( + h)φ (11) ( + h)φ T C = v (12) 5275 km = 12 min km/h In equation (11), l C epesents the visible path length of the satellite. Equation (12) uses the visible path length of the satellite, along with the velocity of the satellite v, to calculate the maximum time that is possible fo a gound station to communicate with the satellite. This is assuming the link budget is adequate.

3 III. MULTICHANNEL SATELLITE SCHEDULING PROBLEM A. Scheduling poblem notation The scheduling poblem notation given in [4] will be used. The notation has the fom: α β 0, β 1,..., β i γ whee α is the machine envionment, β i is the ith job chaacteistic and γ is the optimality citeia. The combination of α, β i and γ in the notation uniquely descibes a specific scheduling poblem. Fo moe infomation on sections III-B, III-C and III-D, see chapte 1 of [5]. B. Machine envionment A machine o seve is the entity in a scheduling poblem that sevices the job. Thoughout this aticle the wod machine is used intechangeably with seve. The machine envionment descibes the chaacteistics of the seves in the scheduling poblem. In single stage machine envionments, jobs ae only pocessed once. This is not to say that jobs may not be pocessed by moe than one machine, but that no job, afte being pocessed, needs to be pocessed again. Two common single-stage machine envionments ae: 1, thee is only one machine and P m, thee ae m paallel identical machines. In the satellite system thee ae twenty-thee channels, whee all channels have equal capacity. In scheduling tems, this is a paallel machine poblem whee the channels ae the machines and all machines ae identical. The channels in which GSL s must be scheduled ae the seves of the system. The numbe of paallel machines is also a constant at m = 23. This shows that the machine envionment is P 23. C. Job chaacteistics Jobs ae units of wok that need to be pefomed. Jobs ae usually entities that need to be seviced/scheduled by some seve o machine. To undestand how to bette schedule jobs, cetain job chaacteistics ae defined to chaacteise diffeent types of jobs. β defines the job chaacteistics in the scheduling notation. Some common job chaacteistics ae: i, each job has a specific elease time, befoe which it cannot be scheduled. d i, each job has a specific due date o deadline, afte which it cannot be scheduled. size i, each job equies a cetain numbe of seves o machines on which it must be scheduled simultaneously. pec, a pecedence elation is given fo each job, fo example job i may only be scheduled afte job x has completed. pmtn, job peemption is allowed, meaning execution of jobs may be halted and esumed late. Gound stations ae discoveed by the satellite and these gound stations have cetain popeties. GSL popeties include name, aveage connection time and the numbe of channels equied. The gound stations that have to be allowed to communicate ae the jobs. These gound station links ae the jobs that need to be scheduled on channels. The gound station links aive ove time and the ode in which links aive as well as the popeties of these links ae assumed to be unknown befoe the actual aival of the links. This assumption is made due to the fact that the obit and position of the satellite is neve pecisely known by emotely situated gound stations. This assumption ceates the need fo an on-line schedule. An on-line schedule leans of new jobs piece by piece. An online schedule will continue to execute as long as thee ae new jobs aiving to be scheduled. In most eal-life examples this is an ongoing pocess. An on-line schedule has no knowledge of futue jobs and thus cannot be made optimal [6]. In an on-line schedule, thee is always a elease date i, befoe which time a job may not be scheduled. A GSL may equie moe than one channel to communicate on. In scheduling tems it may be said that each job may equie moe than one machine. Poblems of this type ae called multipocesso tasks. See ch. 11 in [5]. Fo the satellite scheduling poblem, a gound station may equie anything fom one station to twenty-thee stations, size i = { }. Although it is possible to implement peemptive scheduling, the ovehead switching costs will be too high and a lot of complexity will have to be added to the satellite s administation communication system. In a satellite poject, whee adiation is a poblem, adding ove-optimised code to a system and theeby adding unnecessay complexity, is not consideed good pactice. D. Optimality citeia Fo evey scheduling poblem, some objective function must be minimised. How well the scheduling function is able to minimise the objective function is a measue of the pefomance of the scheduling function. It is possible to achieve an absolute minimum value fo some combinations of objective functions and scheduling algoithms. When this can be done the scheduling scheme is said to be optimal. In objective functions, C i denotes the finishing time of job J i and f i (C i ) denotes the associated cost. The thee most common objective functions ae: n n max{c i i = 1,..., n} C i w i C i i=1 i=1 The fist one is the maximum completion time, also called the Makespan. The second one is the total completion time of all jobs, also called the Total flow time. The thid one is the total weighted completion time of all jobs, also called the Weighted total flow time. Minimisation citeia fo the satellite poblem may be the flow time o the makespan. E. Scheduling poblem statement All sections of the scheduling poblem ae now known. The full scheduling poblem is then: P 23 i, size i = { } C max (13) Equation (13) is a summay of the diffeent sections of the scheduling envionment. Now that the poblem is known, a solution may be found.

4 Geneal link queue Fig. 3. Simulation diagam Dispatche Channel link queue 1 Channel link queue 2 Channel link queue 3 Channel link queue 23 IV. SIMULATION MODEL DESCRIPTION Channel 1 Channel 2 Channel 3 Channel 23 The simulation model was implemented in a Java simulation envionment called Desmo-J [7]. This envionment contains a full suite of simulation stuctues to assist in implementing a simulation model. Desmo-J is a discete simulation envionment [8] whee the use can use eithe event diven o pocess based simulation techniques to implement a simulation model. Pocess based simulation was used to implement this simulato in. This type of simulation consists out of vaious entities, all communicating with each othe, and is best suited fo multipocesso testbeds. Figue 3 shows the implemented simulation model. The entities in the model ae the channels, the dispatche and the gound station links. Anothe entity, which does not appea in the model, is a GSL geneato, to simulate GSL aivals. The queues in the model ae the geneal link queue, the channel link queues, the channel queues and the dispatche queue. The channel queues and the dispatche queue do not show up on the diagam, but these queues ae used to ecod statistics on the idle times of the dispatche and channels. GSL s ae ceated by the GSL geneato and placed on the geneal GSL queue. When the GSL geneato ceates a GSL, it also defines its popeties. These popeties wee descibed in section III-C. The values of these popeties ae sampled fom some distibution, see section IV-A. The GSL geneato only geneates GSL s fo a cetain peiod of time, afte which it switches off. This is to simulate the finite amount of time, a gound station is able to communicate with the satellite fo, in one pass. The dispatche emoves the fist item fom the queue and places it in a channel queue, accoding to some scheduling algoithm. The dispatche has to select both the channel queue, as well as the position in that channel queue. The time that the satellite equies to infom the gound station of the assignment is also taken into account. A channel is assigned to one specific channel queue. It selects a GSL fom its queue and sevices that GSL. Afte a GSL has been seviced, it leaves the system. If a GSL equies moe than one channel, in the simulato, this is handled by copying the GSL pocess and scheduling all of these duplicate pocesses on diffeent channel queues. A. Random numbe steams Thee ae fou andom numbe steams (statistical distibutions) used by the simulato. These ae the inteaival time of GSL s, the aveage connection time of GSL s, the GSL negotiation time and the equied numbe of channels by each GSL. The GSL geneato ceates GSL s, at the times sampled fom the GSL inteaival time time steam, with a equied numbe of channels sampled fom the channel equiement time steam. When a GSL is emoved fom the geneal GSL queue, the dispatche waits fo an amount of time sampled fom the negation time time steam, to simulate the time equied fo the satellite to infom the gound station of the channel assignment. When a channel sevices a gound station, the channel waits fo the amount of time sampled fom aveage connection time time steam, to simulate gound station communications. The inteaival time steam is an Elang distibution. If events occu at some aveage ate, that ate can be modelled as a Poisson distibution. The inteaival time of these events ae modeled as an Elang distibution [9]. The popeties of this distibution wee vaied duing simulation to incease o decease the total amount of GSL s able to connect to the system. The channel equiement steam is an intege exponential distibution, because the majoity of the gound stations will equie few channels, with only a small numbe of stations equiing moe than one to thee channels. The mean of this distibution was set to X = 4,5. The channel negotiation time steam is a Gaussian distibution, because thee is a cetain expected value. This expected value is the time it takes fo a message to be tansmitted down to eath and anothe message to be etuned to the satellite. In section II, this value was computed as t RTT 17 ms. To obtain this type of esponse, a Gaussian distibution with X = 0,017 and σ = 0,0001 was chosen. The aveage connection time is a eal exponential distibution, because gound stations ae expected to usually only communicate fo a shot peiod of time. The mean of this distibution was set to X = 80. Fo moe infomation on the types of distibutions, see [10]. V. THE SCHEDULING ALGORITHM To develop a scheduling algoithm, a base is needed to stat fom. The idea is to define a simple algoithm and then optimise all aspects of the algoithm to incease algoithm pefomance. The main measues of pefomance fo the algoithm ae the aveage queue lengths, the maximum queue lengths, the aveage waiting time of GSL s and how well the algoithm avoids stavation of GSL s To deal with multiple machines, thee ae in fact two scheduling schemes in the system. One scheme deals with channel assignments (level 1 schedule) and the othe scheme deals with detemining the ode in which GSL s assigned to the same channel will execute in (level 2 schedule). Thee ae twenty-thee level 2 schedules, one fo each channel. Thee is one scheduling scheme fo the level 1 schedule and anothe fo the twenty-thee level 2 schedules. A basic level 1 scheduling technique that can minimise the flow time, if the coect level 2 schedule is chosen, is to schedule the next GSL on the fist available machine [11]. Usually this would mean having one queue of customes and when a seve becomes available, anothe job is scheduled onto that seve. In an effot to impove upon this basic technique, queues wee placed befoe each channel. Now the

5 level 1 schedule does not schedule the next job diectly onto a channel, but athe hands that job to the coect level 2 schedule. The level 2 schedule then detemines whee to inset the GSL onto the channel specific queue. This helps in distibuting the wok and complexity of scheduling evenly. The level 1 schedule detemines the next channel queue to schedule on, accoding to shotest length, emoves the fist element fom the geneal GSL queue and hands it to the chosen channels s level 2 schedule. If a GSL equies moe than one channel, it duplicates the GSL s infomation, and hands all the copies to diffeent level 2 schedules. When thee ae no GSL s available, the level 1 schedule blocks to avoid using unnecessay system esouces. A basic fom of the level 2 schedules, is to place all GSL s eceived fom the level 1 schedule into the channel specific queues, as if they wee FIFO queues. Impovements wee made to both the level 1 and level 2 schedules. The fist impovement was to have the level 1 schedule use the sum of aveage completion times, instead of the total length of the queue, to select the next queue. This impovement makes the level 1 schedule moe accuate in selecting the shotest channel queue. The eason being that the numbe of GSL s in the queue does not actually give the tue length of the queue. The tue length of the queue is measued in total communication time. The second impovement was to have the level 2 schedule sot the channel specific queue in a smallest communication time fist ode. The level 2 schedule s job is to maintain the ode of the queue afte evey insetion. This in effect implement a shotest communication time fist scheduling scheme in the level 2 schedule. This, along with the fist available machine scheduling scheme of the level 1 schedule solves the Total flow time optimally fo an off-line schedule [11]. As can be seen fom the simulation esults given in table I, it also impoves the on-line scheduling scheme. The thid impovement was to change the channels selection method. Instead always selecting the fist element in the channel queue, they select the ith element in the queue accoding to an exponential distibution. This means that the fist GSL will still be selected with the highest pobability, but othe GSL s may also be selected. This avoids stavation of lage tasks. VI. SIMULATION RESULTS As stated in section II, the satellite acquies all gound stations in t aq = 2,5 min of its pass ove South Afica. Evey gound station has T C = 12 min of maximum communication time. The Elang distibution modelling the GSL aival ate was set so as to geneate all GSL s in 2,5 min and then switch off. The simulated channel queue length duing one pass of the satelite is shown in figue 4. Duing the fist 2,5 min, all the gound stations ae discoveed. The ate at which gound stations ae seviced, may be obtained fom the slope of the declining numbe of gound stations afte the 2,5 min mak. The steepe this slope is, the bette the scheduling algoithm pefoms. Fig. 4. Channel queue length (s) X= x= Y= y= Channel queue length ove time fo channel queue 0, with 60 GSL s in SCTF, Makespan, D mode System time (s) Channel queue 0 length, with 60 GSL s in SCTF, Makespan, D mode Table I displays the statistics fo all the implemented scheduling schemes. These values wee obtained using a maximum of 60 GSL s o λ = 2 and θ = 2,25 fo the Elang distibution. The maximum wait time is the aveage of the maximum wait times, ove all the channel queues, that a GSL had to wait fo. The aveage wait time is the aveage of the aveage wait times, ove all the queues, that a GSL had to wait fo. The completion time is the time it takes, fom when the fist GSL connects, to the last GSL being seviced. The simulation time was set as 12 min afte the discovey of the last GSL. The stations still waiting to be seviced at the end of the simulation shows how many GSL s will still be waiting fo sevice, on aveage on each channel queue, when the satellite goes out of ange of the last gound station. The modes ae: FIFO, the level 2 schedule always puts gound stations at the end of the channel queue. SCTF, the level 2 schedule maintains a soted queue of GSL s in the channel queue. Q length, the level 1 schedule uses the physical queue length to detemine the channel queue to schedule a GSL on. Makespan, the level 1 schedule uses the total completion time of all GSL s on the queue to detemine the channel queue to schedule a GSL on. Deteministic, a channel always chooses the fist GSL in the channel queue to sevice. Stochastic, a channel chooses the next GSL to sevice fom an exponential distibution that spans the aveage channel queue length. Fom table I, the best time in which all the GSL s can be scheduled in is 950 s = 15,8 min. This is longe than T C = 12 min. This means thee is not enough time to schedule all the gound stations in one pass of the satellite. To be able to schedule all the gound stations, the capacity of the scheduling algoithm should be detemined. This is done by vaying the paametes of the GSL aival ate distibution. All gound stations must be seviced at the end of 2,5 min+ 12 min = 870 s. Fom table I it it seen that the best pefoming algoithm is the SCTF/Makespan/D algoithm, with a aveage waiting time of 265 s. This algoithm has a completion time of 950 s. In othe wods, the time it would take fo the

6 Mode Maximum queue time (s) Aveage queue time (s) Completion time (s) GSL s not seviced FIFO Q length D FIFO Q length S FIFO Makespan S FIFO Makespan D SCTF Q length S SCTF Q length D SCTF Makespan S SCTF Makespan D TABLE I SIMULATION RESULTS FOR VARIOUS SCHEDULING SCHEMES USING 60 GSL S satellite to pocess 60 GSLs, is longe than the communication time window allowed by the obit (950 s > 870 s). To be able to satisfy the equied communication time window citeia, the numbe of gound stations allowed to connect, i.e. the capacity of the satellite, has to be educed. By unning simulations, the maximum numbe of stations that still satisfy the communication time window fo the best pefoming algoithm, was found to be 47. The numbe of stations connecting wee vaied by vaying the paametes of the Elang distibution contolling the aival ate of stations. At 47 GSLs, the Elang distibution has the paametes λ = 2 and θ = 2, 9. The maximum queue time is then 622 s and the aveage queue time is 235 s. When the esults ae compaed, the simplest fom of scheduling (FIFO and Q length) poduce the schedule with the longest aveage and maximum queue times. Using makespan instead of queue length impoves the maximum queue time by 6,3 %, the aveage queue time by 3,4 % and the completion time by 19,4 %. Using SCTF instead of FIFO impoves the maximum queue time by 13,8 %, the aveage queue time by 41,8 % and the completion time by 16,4 %. All the impovements to the basic algoithm impoves the maximum queue time by 15,0 %, the aveage queue time by 40,4 % and the completion time by 29,1 %. No eal impovement benefit can be seen fom using a stochastic scheduling scheme, instead of a deteministic one. In this system, stavation cannot occu. All gound stations ae discoveed ealy on in the system life cycle and then they ae seviced. No new gound stations ente the system afte a cetain point and thus a GSL equiing longe communication time will eventually be seviced. If it is possible to schedule all GSL s in the time window given, the GSL s with longe communication times will also be scheduled. VII. CONCLUSION AND FURTHER WORK It was shown that the gound station allocation poblem can be witten in scheduling tems and modelled in a Java simulation envionment. The final scheduling algoithm can efficiently schedule GSL s on the satellite s communication channels. The simulation esults look pomising, with evey impovement made in the algoithm showing visible impovements in the simulation. It also shows that it is possible to schedule gound station links in eal-time, on a satellite. Futhe wok includes migation of GSL s fom one channel queue onto anothe, to bette distibute the load ove all channels. Othe distibutions should also be investigated and measuements fom actual satellite communication systems can be used to detemine the distibution of GSL aivals. The scheme should also be changed to a weighted scheduling scheme, whee station pioity is taken into account. The metic to optimise would then be the poduct of the connection time and the pioity. Moe exotic scheduling schemes should also be investigated. REFERENCES [1] R. Goss, Multichannel satellite communication and contol system, U.S. Patent , [Online]. Available: za/patents?hl=en\&l=\&vid=uspat [2] R. J. Boain, A-b-cs of sun-synchonous oibt mission design, in AAS/AIAA Space Flight Mechanics Confeence, [3] W. M. Mulaie, Depatment of defense wold geodetic system 1984, its definition and elationships with local geodetic systems, National Geospatial-Intelligence Agency, Tech. Rep., [4] R. L. Gaham, E. L. Lawle, J. K. Lensta, and A. H. G. Rinnooy Kan, Optimization and appoximation in deteministic sequencing and scheduling: A suvey, Annals of Discete Mathematics, pp , [5] P. Bucke, Scheduling Algoithms, 5th ed. Spinge-Velag Belin, [6] J. Y.-T. Leung, Ed., Handbook of Scheduling: Algoithms, Models, and Pefomance analysis. Chapman & Hall/CRC, 2004, ch. 15. [7] Univesity of Hambug. Desmo-j: Discete-event simulation and modelling in java. [Online]. Available: uni-hambug.de/desmoj/ [8] J. M. Gaido, Object-Oiented Discete-Event simulation with Java. Kluwe Academic/Plenum Publishes, New Yok, 2001, ch [9] I. Angus, An intoduction to Elang B and Elang C, Telemanagement, no. 187, pp. 6 8, [10] P. Z. Peebles, Pobability, andom vaiables and andom signal pinciples, 4th ed. McGaw-Hill, Inc., 2001, ch [11] V. T Kindt, J.-C. Billaut, and H. Scott, Multiciteia Scheduling: Theoy, Models and Algoithms. Spinge, 2006, ch John Gilmoe was bon on 17 June, He is cuently a mastes student at the Univesity of Stellenbosch. He obtained his Electical/Electonic Engineeing (with Compute Science) degee, cum laude, fom the Univesity of Stellenbosch in His eseach inteests include: Wieless communication netwoks and hadwae system design. Riaan Wolhute has a B.Sc. B.Eng, M.Eng and a Ph.D. fom Stellenbosch Univesity, and a B.Sc(Eng)(Hons) fom the Univesity of Petoia, in Electonic Engineeing. He is a senio eseache at the Faculty of Engineeing at Stellenbosch Univesity, South Afica.