Scheduling Periodic Information Flow in FieldBus and Multi-FieldBus Environments

Transcription

1 Scheduling Periodic Information Flow in FieldBus and Multi-FieldBus Environments S. Cavalieri, A. Corsaro 2, O. Mirabella, G. Scapellato 2 Università di Catania Facoltà di Ingegneria Istituto di Informatica e Telecomunicazioni Viale A. Doria, Catania (Italy) Tel: , Fax: {cavalieri, omirabel}@iit.unict.it 2 Università di Catania Facoltà di Ingegneria ISA Student Section {ancorsar, scapy}@ tin.it Abstract The paper deals with the scheduling of periodic information flow in single and multi FieldBus environments. The problem is defined from an analytical point of view, giving a brief survey of the most well-known solutions. Then the authors make their contribution to the problem. More specifically, a modification to a well-known single FieldBus scheduling solution is introduced, in order to make its applicability wider. As far as multi FieldBus scheduling is concerned, a genetic approach is presented.. Introduction This paper deals with the problems of scheduling the information flow in communication systems for process control known as FieldBuses. A FieldBus is a serial communication system interconnecting several field devices such as sensors, actuators and PLCs. Examples of FieldBuses are ProfiBus [], FIP [2] and the IEC/ISA FieldBus [3]. The advantages offered by a FieldBus, as compared with a traditional communication system based on the 4-20 ma standard, include simplified wiring, the sharing of resources and simplification of maintenance and documentation [4]. They do, however, present management problems, due to the need to serialise the information traffic produced by the field devices connected to them. This traffic is mostly made up of system variable values, which are updated by producer processes and used by consumer processes. They can be updated periodically or asynchronously. A temperature sensor, for example, samples an analog signal and periodically produces temperature values. An alarm, on the other hand, is a variable the updating of which is unpredictable, i.e. asynchronous. Management of a periodic information flow has to meet two types of constraints. From the viewpoint of the producer process, each variable value has to be transmitted before the new value is produced and written over the previous one. As far as the consumer is concerned, it is necessary to respect the time required to reconstruct the analog signal from the values it receives. If the information flow in a FieldBus is to be managed correctly, it is therefore not sufficient for the producer process to respect its time constraints. Although transmitted within the production period, a variable may, in fact, be received by the consumer

2 process too late for it to be reconstructed properly. Each periodically updated variable is therefore associated with a deadline which takes both the time constraints into account. The scheduling of a periodic information flow has to meet all the variables deadlines. As far as an asynchronous information flow is concerned, it is important for an asynchronously updated variable to be transmitted with a minimum delay. An alarm transmitted with an excessive delay, for example, would have disastrous effects. Periodically updated variables generally have very strict deadlines. Typical values are in the range of a few ms. The delay times asynchronous traffic is allowed, on the other hand, may be as long as a few tens of ms. It is therefore clear that scheduling of a periodic flow is much more critical than that of an asynchronous flow. This paper will thus focus on the management of periodic information flows. Literature provides several approaches to the scheduling of periodic information in a FieldBus communication system. Below we will give a brief survey of these approaches, introducing modifications into some of them to extend the applicability of the strategy concerned to more general cases. Up to now we have only mentioned a single FieldBus system interconnecting several field devices. There are, however, much more complex industrial plants in which the use of more than one FieldBus is indispensable. There are various reasons for this, including the limited length of most FieldBuses, the limited number of field devices a FieldBus can connect, the co-existence of FieldBuses belonging to different communication protocols, and the presence of different modes of transmission (coaxial cable, fibre optics, radio). In such cases a number of FieldBuses are connected with each other by bridges in topologies of varying complexity. This kind of scenario will henceforward be referred to as a Multi- FieldBus environment to distinguish it from a Single FieldBus scenario featuring a single communication system. In a Multi-FieldBus environment scheduling is much more complex, as it is not only necessary to provide for correct management of the information flow produced and consumed locally, but also to manage the flow transiting through several FieldBuses. Devices connected to one FieldBus may, in fact, update the value of a variable that has to be consumed by a device belonging to another FieldBus. The information flow will have to transit on more than one FieldBus, from the one where it is produced to the one to which the consumer process/es is connected. Scheduling is more complex for periodically updated variables whose values have to pass through several FieldBuses because the deadlines are more critical due to the transmission delays incurred. Scheduling in a Multi-FieldBus environment has not been widely dealt with in literature. The aim of this paper is to introduce the problem, define it from an analytical point of view, and provide a solution based on genetic algorithms. A heuristic approach is made necessary by the complexity of the problem, which excludes the possibility of an exhaustive solution. 2. Scheduling in a Single FieldBus Environment The scenario that will be taken into consideration here is the same as the one presented in [5]. It will be assumed that mode with which all the devices gain access to the FieldBus is of the Master/Slave type, where one device takes on the role of Master, controlling the information flow to be transmitted throught the communication system. This occurs by polling the Slave stations and authorising transmission on request.

3 Periodic and asynchronous information flows are managed in two separate time windows, which we will call synchronous and asynchronous windows. During the former periodic traffic is served, while the latter is dedicated to asynchronous traffic. The two windows follow each other cyclically, as shown in Fig.. The figure also gives a definition of a cycle, which is equal to a single sequence of one synchronous and one asynchronous window. The reason for choosing two separate windows is to minimise the cost of context switching between the transfer of periodic traffic and that of asynchronous traffic. Cycle Synchronous Asynchronous time window window Fig. - Synchronous and Asynchronous time windows. As mentioned in the introduction, to guarantee correct transmission of a periodic flow, each periodically updated variable value has to be transmitted at least once before its deadline. The deadline takes into account the time constraints of both the producer and consumer processes. It is defined as the length of each time interval between a generic production instant and the subsequent consumption instant. If these two coincide, the deadline will be taken as equal to the production period of the variable. The problem of scheduling in a single FieldBus environment is to insert the polling for transmission of the periodically updated variables into the synchronous window in such a way that their deadlines are met. Literature provides several solutions. The strategy considered in [5] and in this paper is the one known as multicycle, and will be described in the following section. 2.. Multicycle Polling Scheduling Let us use the following notation: i-th group: Set of variables periodically updated with the same period (i.e. deadline). Ng : Number of groups. n i : Number of variables in the i-th group. T i : Period of the i-th group, which coincides with the deadline for group i. t rr : Data Transition Time for a variable, given by the sum of the time required to poll one variable and that needed to accomplish one data transfer. The values of all the variables are assumed to be of the same size. The t rr value is therefore the same for all the groups. The groups are ordered in ascending order by their deadline, so the group with the index has the most urgent deadline. In [5], all the deadlines are rounded up/down to multiples of the deadline for group. If this is 20ms, for example, and a generic deadline is 30 ms, it is rounded down to 300ms. The length of each cycle thus coincides with the deadline for group and is called a primary cycle; the deadline for a generic group with the index i, called a secondary cycle, is T i =k i *T, where K i N. In the rest of this paper the hypothesis formulated in [5] will be extended to the more general case in which all the deadlines can take arbitrary values with the respect of the

4 deadline for group, thus greatly broadening the field of applicability of multicycle scheduling. On the basis of this new hypothesis the length of each cycle, which is still called a primary cycle, is equal to the maximum common denominator (MCD) of all the deadlines. In multicycle scheduling each time window making up the primary cycle is divided into a certain number of slot times, each lasting t rr. If N Smax is the number of variables to schedule in the synchronous time window, the length of this window will be T Smax =N Smax. t rr. The scheduling of the periodic information flow consists of determining the complete polling sequence in each synchronous time window, such that all the deadlines are met. It is also necessary for N Smax to be minimised so that the number of slot times for the asynchronous flow is maximised. These two objectives can be achieved by means of an algorithm that determines the polling sequence in each synchronous time window on-line, during the evolution of the system. There are various algorithms for this purpose, classified as static and dynamic algorithms according to whether the length of the synchronous time window is considered to be constant or not. Below we will consider only some of the best-known static algorithms Priority Algorithms Some of the most interesting static algorithms are priority algorithms. They try to solve the problem of multicycle scheduling by assigning each task a given priority and thus performing priority-based scheduling. In [5] two priority algorithms are presented, based on the Rate Monotonic (RM) [6] and Earliest Deadline First (EDF) algorithms [7]. They are called the Rate Monotonic Multicycle (RMM) and Earliest Deadline First Multicycle (EDFM) algorithms. They both comprise three steps: Calculation of the maximum number of variables to schedule in a primary cycle, i.e. N Smax. Calculation of the priority to assign to each group of variables. Main Polling Algorithm. We have made substantial modifications to the first of these three steps, introducing a new way to calculate the value of N Smax, and extending the calculation to cover cases in which the deadlines for the groups with an index greater than are not whole multiples of the deadline for group. As the remaining two steps are the same as those illustrated in [5], they will not be described here; for further details the reader is referred to [5] Calculation of N Smax for the Primary Cycle The calculation of N Smax in the primary cycle is different in the RMM and EDFM algorithms. In RMM algorithm, if the period T i is a integer multiple of the period T j where i>j, the value of N Smax is given by: N g n i N Smax = Pc i= Ti where P c is the primary cycle, equal to T. In a general case where the deadlines have arbitrary values, the value of N Smax is given by:

5 i n j T i NSmax = Pc max i N j= Ti T g j where P c is the primary cycle, equal to the MCD of the deadlines. In the EDFM algorithm, in the general case where all the deadlines of the groups with an index higher than take arbitrary values as compared with the deadline for group, the value of N Smax is given by: N g n i N Smax = Pc i= Ti where P c is the primary cycle, which is equal to T, if the deadlines for the groups with an index greater than are integer multiples of T, or to the maximum common denominator in the more general case. 3. Scheduling in Multi-FieldBus Environments As said in the introduction, the term Multi-FieldBus indicates a system in which there are several independent FieldBuses (each with its local periodic and asynchronous traffic), interconnected in arbitrary topologies by means of bridges. In these environments, one or more devices need to receive the system variable values produced by devices connected to remote FieldBuses, which can be accessed by particular routing sequences. As in the Single FieldBus scenario, management of the information flow crossing several FieldBuses has not only to guarantee that the values of each variable will be transmitted during their production period, but also that they are delivered to the consumer process before its consumption time expires. This is much harder in a Multi-FieldBus scenario, due to the propagation delays caused by the need to cross more than one communication system.. Henceforward, the variables that have to cross several FieldBuses will be called End- To-End (ETE) variables. Each one has an End-to-End deadline (ETE deadline) which, as in the Single FieldBus scenario, will coincide with the variable updating period. The aim of scheduling in a Multi FieldBus environment is to deliver each ETE variable value to the consumer process before its ETE deadline, i.e. the sum of its transmission times, from the original FieldBus to its destination, must be less than the ETE deadline. The parameters on which to act to solve the problem are two: management of the ETE variables in each FieldBus and choice of the route between the source and destination FieldBuses. Both parameters have an important role in solving the problem. Correct management of the flow of ETE variables in each FieldBus, in fact, allows the ETE deadlines to be met. Choice of the routing that minimises the distance between the source and destination Fieldbuses, on the other hand, reduces the propagation delays, thus also ensuring that the ETE deadlines are met. The presence of two degrees of freedom in solving the scheduling problem makes it even more complex. One will therefore be eliminated in what follows. It will, that is, be assumed that the routing sequence is unequivocally fixed. The only parameter to be modified to solve the problem of scheduling in a Multi- FieldBus environment is therefore the local scheduling of the ETE variables in the single FieldBuses belonging to the routing sequence chosen. Scheduling is performed by considering the ETE variables, in each FieldBus they cross, to be periodically updated variables with a deadline lower than the ETE deadline. This deadline is assigned according to the length of

6 bandwidth available in each FieldBus, as will be explained in the following section. Of course, the sum of the deadlines of the FieldBuses belonging to the routing sequence has to be less than or equal to the ETE deadline. Once the local deadlines have been set, scheduling in a Multi-FieldBus environment is the same as in a Single FieldBus one, using one of the approaches illustrated in the previous section. We chose to use the Earliest Deadline First algorithm. In the following section we formalise the problem of scheduling in a Multi-FieldBus environment. 3.. Formalisation of Multi-FieldBus Scheduling Let n be the number of interconnected FieldBuses and let there be m ETE variables, each of which has a particular routing sequence and ETE deadline. The variables are subdivided into groups in such a way that all those belonging to the same group have the same routing sequence and ETE deadline. Put more formally, each group, g i, i=,..r (where r is at most equal to the number of ETE variables, i.e. m), is defined by the following n-tuple (ETED i, r i, d i, n i ), where ETED i is the ETE deadline for the i-th group, n i is the number of variables belonging to the group i, r i =[r i, r i2,...,r in ] T, and d i =[ d i, d i2,..., d in ] T, with: if variables belonging to group i involves FiedlBus j r ij = 0 otherwise deadline of variables belonging to group i infiedlbus j,if rij 0 d ij = 0 if rij=0 The aim of scheduling in a Multi-FieldBus environment is to determine the matrices R = {r i } i=..r and D = {d i } i=..r. As said previously, to simplify the problem the degree of liberty concerning choice of the routing sequence is eliminated, the sequence being fixed. Determination of the matrix D, i.e. the deadlines in the FieldBuses crossed by the ETE variables, has to be such that meeting each of these deadlines allows the ETE deadline to be met. The information flow also has to be uniformly distributed in the various FieldBuses involved. To check whether these two conditions are met, we have introduced a parameter called a Schedulability Factor (SF) which measures the workload on each FieldBus. With this parameter it is possible to choose the deadline on each FieldBus and to distribute the ETE flow uniformly over the different FieldBuses. The Schedulability Factor is normalised to, so a lower value means that the FieldBus for which the SF is calculated still has sufficient bandwidth available for asynchronous traffic. A value greater than means that the periodic flow is impossible to schedule as it would require more bandwidth than is available. The SF is calculated by means of the following steps, according to the specification of the groups of local and ETE variables, the deadline of each of which is known (more specifically, the deadline for the local variables coincides with the variable refresh period, and that of the ETE variables in each FieldBus is given by a possible solution to the Multi-FieldBus scheduling problem). The MCD for all the local and ETE variable deadlines for that particular FieldBus is calculated. For each period of time equal to this MCD, the ratio between the number of available slots and the number of slots needed to schedule the traffic is calculated. This is done until the time value reached is equal to the least common multiple (LCM) for all the deadlines. The highest ratio value is taken as the schedulability factor.

7 Scheduling in a Multi-FieldBus environment can thus be formalised as follows: minimise (σ(sf j )) subject to: n rij dij ETEDi, i [,.., r] j= SFj where j=,..,n, and r is the number of groups Scheduling by a Genetic Approach Multi FieldBus scheduling becomes extremely complex as the number of FieldBuses and ETE variables grows. A heuristic approach is therefore highly appropriate. We propose to use a solution based on genetic algorithms. In the following section we present the coding and operators introduced to apply Genetic Algorithms to the problem being examined Coding of the Solution The coding used is a vector of integers which is logically divided into a number of subvectors equal to the number of ETE variables to be scheduled. Each vector is equal to the number of FieldBuses the relative ETE variable has to cross. Each integer in the subvectors represents the deadline for the ETE variable in the FieldBus corresponding to the subvector element Fitness The fitness function mainly depends on the value of the schedulability factor in each FieldBus and the variance of all the schedulability factors. We have also expressed the fitness function in terms of the distance between the local deadlines of the ETE variables passing through the generic FieldBus. The fitness function giving the best results is given by the following formula: ( (SFmax SFmin )) k b f (I) = ( SFmax ) + + ( SF) k a ( Dmax D + a) where I is a generic individual in the population, the parameters k a, k b and a are userselected, SF max, SF min, SF are the maximum, minimum and average values of SF for all the FieldBuses, and D max and D represent the maximum and average distance between the local deadlines for the ETA variables, considering all the FieldBus. This fitness function is evaluated if the solution is feasible. The validity of the solution is checked by using the following penalty function:

8 n, if i : rij dij > ETEDi j= P(I) = h 00 where h = j f (I) otherwise { SF : j n and SF > }, j n if rij dij ETEDi, i [..r] j= Crossover The crossover operators presented in the literature can be used without any modifications Smart Mutation This operator was defined ad hoc for Multi-FieldBus scheduling, as classical mutation operators are not suitable for the problem at hand. The modifications made to the individuals in each population are as follows: For each FieldBus whose SF is greater than, a group of variables is chosen at random and the deadline is set to a random number in the interval between the current deadline and the ETE deadline. In FieldBuses with an SF lower than, a group is randomly chosen and the deadline is set to a randomly generated number in the interval between and the current deadline. An interval (in the chromosome) is randomly set and the gene with the highest value is selected; it deadline is then fixed to a random number between and the current deadline An Example of Multi-FieldBus Scheduling by the Genetic Approach The aim of this section is to give an example of how the genetic algorithm operates. Let us consider the 5-FieldBus system shown in Fig.2. F F2 F3 F4 F5 Fig.2 - A communication system made up by five FieldBuses It is assumed that the local traffic in each of the five FieldBuses is expressed by the following percentages of occupied bandwidth as compared with the amount available (which is Mbps

9 in all the FieldBuses except F, where it is 2 Mbps): 0.52, 0.44, 0.44, 0.44, The end-to end traffic comprises 4 groups of variables, the characteristics of which are given in Table. The routing sequence chosen is established by the topology in Fig.2. The parameters used for the genetic algorithm are: a population of 50 individuals, a Mating Pool of 30, a Tournament Selection of 5, a crossover probability of 0.8 and a mutation probability of 0.7. The parameters K a, K b and a are set to 5, and 0. respectively. Finally it was assumed that each ETE variable transmitted was 64 bits in length. Table - Time characteristics of ETE variables Group n i ETED i Source Destination Routing 4 5 F F4 F,F2,F F F5 F,F3,F F4 F5 F4,F2,F,F3,F F5 F4 F5,F3,F,F2,F4 The graph in Fig.3 shows the trend of the fitness function during evolution of the population. As can be observed, it improves in the very first evolutions. The graph in Fig.4 shows the maximum, average and minimum SF for the 5 FieldBuses. As can be seen, when the evolutions increase these values tend to converge, in agreement with one of the aims of the genetic algorithm, which tries to distribute the workload uniformly over the system Generation Fitness Fig.3 - Values of Fitness function versus the number of generations A final consideration relates to the capacity of the approach presented to modify the local deadlines of the ETE traffic, so as to reduce the parameter SF and thus improve the fitness function. Let us consider the fittest individual in the population for the 95th generation. This individual is:,3, 2,2,2 2,,,5,,5,5,3,5. Note the subdivision in the coding of the individual on the basis of the 4 ETE variables. The fitness function corresponding to this individual is , and SF is The genetic approach is capable of improving the SF simply by modifying the local deadlines. The fittest individual in the next generation, in fact, is :,2,2 2,2,2 2,,,5,,5,5,3,5, differing from the previous one only in the

10 modification of the deadlines in FieldBuses F2 and F4 for the ETE variables in group. The fitness function corresponding to this individual is , and SF is ,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0, Generation 08 Max SF Average SF Min SF Fig.4 - Values of maximum, minimum and average SF versus the number of generations Conclusions This paper has had a dual aim. On the one hand the problem of periodic flow scheduling in a Single FieldBus system has been dealt with. Some of the best-known solutions to the problem have been illustrated, proposing modifications to extend their applicability. Then the problem of scheduling in a Multi-FieldBus environment has been tackled, giving an analytical definition of the problem and proposing a heuristic solution based on genetic algorithms. References [] German Institute of Normalization, "Profibus Standard Part and 2", DIN 9 245, 99. [2] French Association for Standardization, "Bus FIP for Exchange of Information between Transmitters, Actuators and Programmable Controllers", NF C46, documents , 990. [3] IEC 65C WG6, Digital Data Communications for Measurement and Control Working Group 6: FieldBus Standard for Use in Industrial Control Systems, Part : Introductory Guide. [4] P.Pleinevaux, J.D.Decotignie, "Time Critical Communication Networks: FieldBuses", IEEE Network Magazine, Vol.2, No.3, 998. [5] P Raja, G.Noubir, "Static and Dynamic Polling Mechanism for FieldBus Networks". ACM Operating System Review, 27(), 993. [6] C.L.Liu, J.W.Layland, "Scheduling Algorithms for Multiprogramming in Hard Real Time Environment", JACM, 20():46,6, 973. [7] E.L.Lawler, J.M.Moore, "A Functional Equation and its Application to Resource Allocation and Scheduling Problem", Management Science, Vol.6, pp.77-84, 969.