Scheduling for a TTCAN network with a stochastic optimization algorithm

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1 Schedulng for a TTCAN network wth a stochastc otmzaton algorthm JosŽ Fonseca*, Fernanda Coutnho**, Jorge Barreros** * ET / IEETA Ð Unversdade de Avero, Portugal ** Insttuto Sueror de Engenhara de Combra, Portugal The TTCAN rotocol s a new develoment n CAN technology that secfes a tme-slot based communcaton mechansm. TTCAN technology avods the transmsson collsons commonly found n standard CAN networks. In TTCAN, all the message nstances are transmtted only on revously allocated tme-slots. No other nstance may be transmtted on an allocated tme-slot, so transmsson collsons are avoded. Before transmttng a message set over a TTCAN network, t s necessary to create a vald schedulng table that secfes how the tme s dscretzed nto tme-slots and how the message nstances are allocated nto those tme-slots. Buldng a vald otmzed schedulng table that follows the TTCAN secfcaton snõt trval. Addtonally, several dstnct schedulng tables may be bult for the same message set, so t s necessary to use some qualty crteron to select one among all. Tycal message sets nclude a large number of messages, makng manual schedulng a very hard and error-rone rocess. Ths means t s desrable to use automated tools that comute a feasble schedulng table automatcally for a gven message set. In ths aer, we resent a schedulng tool for TTCAN networks that generates a vald schedulng table usng a stochastc otmzaton algorthm. The tool attemts to otmze the schedulng table so t wll generate solutons wth low jtter. The tool was aled to two well known message sets used n the automotve ndustry and results are ostve.. Introducton The CAN feldbus has been used n automotve ndustry for real-tme dstrbuted systems embedded n vehcles snce several years. Recently, the nterest of the ndustral and research communtes n communcaton based on the tme-trggered aradgm [] has ncreased substantally and a standardzaton rocess led to the defnton of a new sesson layer for CAN. The future standard, known as tme-trggered CAN (TTCAN) [4] uses a schedulng table that must be bult off-lne, ror to the system start of oeraton. In ths aer, we resent an early verson of a tool that can be used to smlfy the constructon of the requred schedulng table. We begn wth a bref resentaton of the TTCAN rotocol, and then we follow by descrbng the scheduler and otmzer algorthms. We brefly descrbe the tool oeraton and some of ts screens. We show some results obtaned from alyng the tool to a modfed PSA message set [3] wth messages havng harmonc erods. The results are brefly analyzed, some conclusons are extracted and some future work s dentfed. 2. TTCAN Ð Tme-trggered CAN urng the last years, CAN Ð Controller Area Network has become the man feldbus used n the tme crtcal arts of automotve systems. Although CAN oerates followng the eventtrggered aradgm, recent academc studes [8] onted to the ossblty of usng a tmetrggered aroach n art of the oeraton of CAN based dstrbuted systems. Ths feature could mrove the bandwdth utlzaton n CANbased real-tme systems by searatng the erodc traffc from the aerodc one and keeng the tmelness guarantees of the former. From the ndustral sde, the nterest of usng the tme-trggered aroach n CAN has also been recognzed snce some tme and, as a consequence, a standardzaton task force (ISO/TC 22/SC 3/WG /TF 6) was launched under Internatonal Standards Organzaton n order to acheve a defnton for a sesson layer for CAN. Ths standard, whch wll be numbered 07-0

2 898-4, s already known as TTCAN, from Tme-Trggered Controller Area Network. In TTCAN, a secal node, the tme master, s resonsble for the transmsson of a systolc message, the reference message, whch s used to acheve synchronzaton between the feldbus nodes. The reference message marks the start of a tme slot called the Basc Cycle (BC). The BC may be dvded n dfferent tyes of wndows, namely, the exclusve wndows and the arbtratng wndows. An exclusve wndow s used to transmt a secfc erodc message. An arbtratng wndow may be used to transmt any message, rovded t gans the btwse arbtratng rocess as n normal CAN oeraton and rovded t fnshes transmsson before the end of the wndow, thus guaranteeng temoral solaton between the dfferent tyes of traffc. The comlete traffc attern n a TTCAN system conssts n a fxed number of consecutve BCs and s named the System atrx or atrx Cycle (S). In fgure, an examle of a system S s resented. There, t s ossble to notce one of the major restrctons n the S constructon, whch s the column lke organzaton. All the wndows of the same column n every BC must be of the same sze. Wth ths organzaton t s ossble to defne a set of trgger nstants (offsets from the reference message) whch s ket constant from BC to BC all along the S, thus smlfyng the TTCAN controllers hardware. Once the C s defned, t s ossble to merge two (or more) consecutve arbtratng wndows n the same BC n order to facltate the transmsson of normal CAN messages. Fnally, The other major restrcton s n the number of BCs er S, whch must be an nteger ower of two. BC essage A B Arbtraton Wndow C essage essage essage A AW Arbtraton Wndow E A B Arbtraton Wndow C A AW - Arbtraton Wndow BC - Basc Cycles A, B, C,, E, F - Perodc essages Transmsson Columns Arbtraton Wndow Fgure Examle of a atrx Cycle n TTCAN. In TTCAN, the system matrx must be defned off-lne. All the nodes must have stored the corresondent nformaton ror to the start of E F oeraton. etals about TTCAN oeraton modes, synchronzaton technques and other secfcaton detals can be found n [4], [5] and n the draft standard. 3. Buldng a schedule The rocess of off-lne schedulng a message set n the case of a TTCAN network conssts n buldng the system matrx (S). It ncludes: The determnaton of the number of columns. The determnaton of the number of rows. The defnton of the duraton of each column. The ndcaton of the message to be transmtted n each cell (row, column). Ths must be done resectng the messagesõ erod and duraton. In what concerns the erod, the frst aroach s to kee the average erod of each message dentcal to the resectve nstantaneous erod. Ths s done usng the arorate number of message nstances n the system matrx. The average erod s equal to the duraton of S dvded by the number of message nstances. In what concerns the messagesõ duraton, ths determnes the column wdth. In ste of these restrctons and of the one mosed to the number of Basc Cycles as ndcated n secton 2, t s usually ossble to buld several dstnct system matrxes for the same message set. Consequently, t s ossble to assess the qualty of the schedule n the System atrx accordng to some re-defned crteron. In the resent case we use a cost functon based on the sum of the message jtter values. Jtter s determned for every nstance of every message all over the system matrx. The cost functon s weghted by the system matrx duraton. The corresondent exresson s the followng: Jtter = e a where e s the exected begnnng tme of transmsson of nstance of message, a s the actual begnnng tme and s the duraton of the system matrx. 07-

3 Consderng now the automatc tool oeraton, the requred hases needed to buld the system matrx are the followng: Schedulng. Otmzaton. The frst corresonds to the generaton of a feasble set of dstnct system matrxes (Ss). The second does the selecton of the best Ss accordng to the cost functon above. In order to be able to mantan the average erod of every message, the Ss duraton,, must be the least common multle of the messagesõ erods (t could also be an nteger multle of t). The average erod s ket wth / P nstances of every message of erod P durng the S. The frst hase, schedulng, ncludes the followng stes:. etermnaton of the maxmum number of lnes of the system matrx. 2. essage allocaton. 3. Free tme redstrbuton. Ignorng the restrcton about the number of basc cycles, t s obvous that the maxmum number of lnes n the S s bounded by: L max = T where T max s the maxmum transmsson tme of all the messages n the set. Before startng the allocaton rocess, the automatc tool generates an ordered set I whch ncludes every nstance of every message n the ntal set. Ths set s organzed by decreasng order of the message transmsson tme T : max I I I 2 K K I I 2,,...,,,..., I,..., I,..., I K = { n 2 2 n n } T = T > T >... > max The next ste n the oeraton of the tool conssts n defnng a random number of lnes: L 2 L max Then, the tool removes the frst L nstances n I and allocates them n the frst column of the system matrx. The tool reeats ths last ste untl all nstances n I are removed, thus obtanng a S wth the followng number of columns, # C : # I # C = L As the longer messages are taken nto consderaton frst, # C s mnmum. At ths moment t s ossble to determne the mnmum duraton of the basc cycle for ths artcular system matrx: BC = # C = wth beng the duraton of each column. Wth ths value t s ossble to determne f the set s schedulable whch haens when: BC L T n wth n beng the number of dfferent messages n the ntal set and: If the set s schedulable then there s some free tme avalable n each basc cycle: K = and P t free = L BC 07-2

Otmzaton rocess The otmzaton rocess uses a set of feasble system matrxes bult as descrbed revously.

4 The tool nserts a free column between each two occued columns and redstrbutes the free tme randomly between the frst ones. Ths s the only random factor n the constructon of the frst set of system matrxes. Fgure 2 - Examle of a frst System atrx, after an ntal random transformaton. 3. Otmzaton rocess The otmzaton rocess uses a set of feasble system matrxes bult as descrbed revously. These matrxes, consdered the ntal oulaton n a smlar way to genetc algorthms, wll be subject to random transformatons. These transformatons must guarantee that the matrxes are stll feasble afterwards. The cost functon defned above determnes the qualty of the matrxes. The comlete set of stes n ths rocess s the followng:. Generaton of the ntal oulaton; 2. versfcaton of the oulaton; 3. Random selecton of a matrx; 4. Alcaton of a random transfor-maton to the selected matrx; 5. Evaluaton of the cost functon for ths matrx. 6. If ths matrx s worse than the worst matrx n the oulaton then t s elmnated, otherwse t relaces the latter; 7. Reeat stes 4 to 6 tll the re-defned maxmum number of teratons s attaned. Consderng ste, the number of elements that consttute the ntal oulaton s defned revously by the user. The scheduler generates then a feasble system matrx as t was exlaned before. In ste 2 the tool ales to the elements of the oulaton a random transformaton wthout carng about qualty. Ths orgnates some dversty n the ntal oulaton. Ths oeraton ends the ntalzaton rocess. Now the man body of the otmzaton algorthm s attaned. The algorthm s based on a steady state genetc algorthm [6], [7]. However, we called t a stochastc algorthm, as we couldnõt fnd any smle rocess to aly crossover keeng the system matrxes feasble. Another ssue regardng the comleton of the algorthm s the number of teratons. In fact, t s mossble to defne an absolute value for the cost functon that could be used n every message set. Jtter deends on the transmsson load and on the relatonsh between the messagesõ erods. The number of teratons must then be re-mosed by the user. It s easy to choose an adequate value after runnng a coule of otmzaton rocesses. 4. A bref look at the tool and some results Before startng the oeraton of the tool, the otmzaton settngs must be ntalzed (fgure 3). These are the number of runs, the number of teratons, the sze of the ntal oulaton and the robabltes of each transformaton. Fgure 3 Ð Intalzaton of arameters. After, a message set must be chosen from a fle or a new one must be created. The tool has also the adequate edtng screen (fgure 5). 07-3

5 When ths s done, t s ossble to run the otmzaton tests. When the message set has not too many messages, the user can get a flavor of the fnal otmzed schedule drectly from the man tool screen (fgure 6). The accurate results can be obtaned from an outut fle. An examle s shown n fgure 4. In [9] t was shown that the otmzaton tool was able to schedule the well known SAE [2] and PSA [3] message sets whch are often used as benchmarks for feldbus based dstrbuted systems. The messages n the sets have nonharmonc erods so, t s only ossble to reduce jtter, whch was acheved by the tool, but t s mossble to elmnate t. In order to verfy f the tool s able to fnd a zero jtter soluton, we decded to use a modfed PSA message set n whch the messagesõ erods were slghtly reduced n order to become harmonc. The messagesõ arameters are the ones n fgure 5. notced also many solutons wth a very reduced jtter and some wth jtter n two or three messages. It was clear that the number of teratons was enough to arrve to a steady oulaton, so we thnk that the otmzaton often dscovers just a local mnmum. However, as the tme to execute s just a few seconds n a normal PC, t s quck to make a reasonable number of otmzatons and t s almost sure that a good schedule s found. Confg Po sze:0 Nr of teratons:20000 Probabltes column swa:20 cell swa:20 free tme dstrb:20 horz mrror :20 vertcal mrror :20 Rows:8 Columns:2 Column duraton: Schedulng matrx: (- reresents an emty cell, other values are the ndex of the message (wth the same order that was defned n the nut fle)) Jtter:0 Fgure 4 Ð Schedule wth 0 jtter (outut from the tool). Some tenths of smulatons were then made wth that set. Several zero jtter solutons such as the one n fgure 4 were obtaned. We 07-4

Fgure 5 Ð Vew of the Create/Edt message screen wth the modfed PSA set. Fgure 6 Ð an screen of the tool showng a schedule wth 0 jtter (outut from the tool). 5. Conclusons We develoed a schedulng and otmzaton tool caable of buldng the so-called system matrx for a TTCAN based network gven a set of erodc messages.

An otmzaton hase ales dfferent transformatons to the schedule n order to refne the soluton so that message jtter can be reduced or, f ossble, elmnated.

6 Fgure 5 Ð Vew of the Create/Edt message screen wth the modfed PSA set. Fgure 6 Ð an screen of the tool showng a schedule wth 0 jtter (outut from the tool). 5. Conclusons We develoed a schedulng and otmzaton tool caable of buldng the so-called system matrx for a TTCAN based network gven a set of erodc messages. The tool, based on a stochastc algorthm smlar to a genetc one, always generates a vald schedulng soluton for feasble sets. An otmzaton hase ales dfferent transformatons to the schedule n order to refne the soluton so that message jtter can be reduced or, f ossble, elmnated. The tool has been tred wth SAE and PSA message sets and could fnd several zero jtter schedules wth a modfed verson of ths last set. 07-5

7 However, there s yet some research work to do on t. Frst, we would lke to tune some ntal arameters such as the ercentages of the otmzaton transformatons. Also, we would lke to fnd more of those transformatons and to study the ossblty of alyng a transformaton smlar to the crossover oeraton n genetc algorthms. JosŽ A. Fonseca ET/IEETA, Unversdade of Avero Camus Unverst ro de Santago P Avero Ð PORTUGAL Phone: Fax: Emal: jaf@det.ua.t s [] Koetz H., ÒReal Tme Systems - esgn Prncles for strbuted Embedded AlcatonsÓ, Kluwer Academc Publshers, 997. [2] Tndel K., Burns A., ÒGuaranteeng essage Latences on Control Area Network (CAN)Ó, Proceedngs of the ICCÕ94, anz, Germany, 994. [3] Navet N., Song Y.-Q., ÒPerformance and Fault Tolerance of Real Tme Alcatons strbuted over CANÓ, CA Ð CAN n Automaton Research Award, 997. [4] FŸhrer T., et al, ÒTme-trggered Communcaton on CAN (Tme-trggered CAN- TTCAN)Ó, Proceedngs of ICCÕ2000, Amsterdam, The Netherlands, [5] Hartwch F., et al, ÒCAN Network wth Tmetrggered CommuncatonÓ, Proceedngs of ICCÕ2000, Amsterdam, The Netherlands, [6] Coutnho F., et al, ÒUsng Genetc Algorthms to Reduce Jtter n Control Varables Transmtted over CANÓ, Proceedngs of ICCÕ2000, Amsterdam, The Netherlands, [7] chalewcz Z., ÒGenetc Algorthms + ata Structures = Evoluton Programs (3rd, revsed and extended edton)ó, Srnger-Verlag. Berln, 999. [8] Almeda L., Fonseca J., Fonseca P., ÒA Flexble Tme-Trggered Communcaton System Based on the Controller Area NetworkÓ Proceedngs FeT '99 - Feldbus Systems and ther Alcatons Conference, agdeburg, Germany, Setember 23-24, 999. [9] Coutnho F., Barreros J., Fonseca J., ÒSchedulng for a TTCAN Network wth a Stochastc Otmzaton AlgorthmÓ, roceedngs of 4 th FETÕ200, IFAC Conference on Feldbus Systems and ther Alcatons, Nancy, France, November 5-6,

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