ساخت موارد زمان توزیع چگالی احتمال در یک مدل جریان کاری

This paper presents a method to judge whether a business process is successful or not. A business process is deemed successful if a large enough proportion of instances dwell in a workflow (wait and be executed) for less than given period. By analyzing instances’ dwelling time distribution in a workflow, the proportion of instances which dwell in the workflow for less than any given period will be achieved. The performance analysis of workflow model plays an important role in the research of workflow techniques and efficient implementation of workflow management. It includes the analysis of instances’ dwelling time distribution in a workflow process. Multidimensional workflow net (MWF-net) includes multiple timing workflow nets (TWF-nets) and the organization and resource information. The processes of transaction instances form a queuing model in which the transaction instances act as customers and the resources act as servers. The key contribution of this paper is twofold. First, this paper presents a theoretical method to calculate the instances’ dwelling time probability density in a workflow where the activities are structured and predictable. Second, by this method the analysis of instances’ dwelling time distribution and satisfactory degree based on dwelling time can be achieved. The service time of an instance is specified by the firing delay of the corresponding transition (executing time of the corresponding activity). It is assumed that the service request (processing of a transaction instance) arrives with exponentially distributed inter-arrival times and the firing delay of a transition (executing time of the corresponding activity) follows exponential distribution. Then, the instances’ dwelling time probability density analysis in each activity and each control structure of a workflow model is performed. According to the above results a method is proposed for computing the instances’ dwelling time probability density in a workflow model. Finally an example is used to show that the proposed method can be effectively utilized in practice.

Workflow technology is good for achieving a process oriented view of the organization and subsequently process automation. Workflow management is an effective means realizing full or partial automation of a business process (Fan, 2001). A business process is a set of one or more linked procedures or activities that collectively realize a business objective or policy goal, normally within the context of an organizational structure defining functional roles and relationships (Fan, 2001). Despite the abundance of workflow management systems developed for different types of workflow based on different paradigms (Adam et al., 1998, Sadiq and Orlowska, 2000, van der Aalst, 1998 and van der Aalst and ter Hofstede, 2000), the lack of rigorous theoretic foundation and then effective model verification and analysis methods has blocked workflow techniques’ research and application (Li et al., 2004, van der Aalst, 2003 and van der Aalst et al., 2007). The rationality and correctness analysis should be carried out from four aspects that are relevant for workflow modeling and workflow execution: process control logic, timing constraint logic, resource dependency logic, and information dependency logic (Li et al., 2004 and van der Aalst et al., 2000). The correctness analysis of process control logic aims to avoid the deadlocks or structural conflicts in the execution of a workflow model caused by the errors in its process control. Some verification and conflict detection methods have been discussed in Workflow Management Coalition, 1998, van der Aalst and ter Hofstede, 2000, Han et al., 1996, Hu, 2001, van der Aalst, 2003, Sadiq et al., 2005, Shazia., 2005, Sadiq and E.Orlowska, 1997 and Hofstede and Orlowska, 1999. The objective of resource dependency logic verification is to prove correctness of the static or dynamic resource allocation rules and consistence with the process control logic. The information dependency logic cares about the internal consistence of a workflow-related data and the correctness of temporary relation among different workflow application data. The timing constraint verification and analysis deal with the temporal aspects of a workflow model such as deadlines (Panagos et al., 1997, Pozewauning et al., 1997 and van der Aalst et al., 2007), time scales (Marjanovic, 2000, Marjanovic and Orlowska, 1999a, Marjanovic and Orlowska, 1999b, Qu et al., 2002, Sadiq et al., 2000, van der Aalst et al., 2000 and Zhuge et al., 2001) schedulability analysis (van der Aalst, 1996), and boundedness verification (Li, Fan, & Zhou, 2003) and time violation handling (Eder, Panagos, Pozewaunig, et al., 1999, Eder, Panagos, Rabinovich, 1999 and Sadiq, Orlowska, Sadiq, Schulz, 2005). Quality of Service in Flexible Workflows is discussed in Sadiq et al., 2006 and Sadiq, Orlowska, Sadiq, Lin, 2005. The above analysis can ensure only the functionally working workflow (correctness) but not its operational efficiency. The performance level (Eder, Panagos, Pozewaunig, et al., 1999, Eder, Panagos, Rabinovich, 1999, Ferscha, 1994a, Ferscha, 1994b, Kevin et al., 2002, Li et al., 2004, Lin et al., 2002, Schomig and Rau, 1995, Son and Kim, 2001, van Hee et al., 2000 and Yamaguchi et al., 2000),on the other hand, aims to evaluate the ability of the workflow to meet requirements concerning some key performance indicators such as, maximal parallelism, throughput, service levels, and sensitivity. The analysis of resource availability and utilization, and average turnaround time is performed at this level. Performance analysis of workflow has not get enough attention of researchers commensurate with its importance until now (Salimifard & Wright, 2001). The performance analysis of a workflow model (business process) is different from that of WfMS architecture (Gillmann et al., 2000 and Kim and Ellis, 2001). The performance analysis can be conducted only after the rationality and correctness analysis has been carried out. So it is assumed that there are no temporal and logical errors in the considered workflow models at the performance analysis stage. PN are the only formal techniques able to be used for structural modeling and a wide range of qualitative and quantitative analysis (Salimifard & Wright, 2001). PN-based workflow management systems are widely used because of formal semantics, local state-based system description, and abundant analysis techniques (van der Aalst & et al., 1998, chap. 10). So PNs are a naturally selected mathematical foundation for the formal performance analysis of workflow models. Many researchers use PN techniques to study workflow (Adam et al., 1998, Ferscha, 1994a, Ferscha, 1994b, Han et al., 1996, Hu, 2001, Li et al., 2003, Lin et al., 2002, Panagos et al., 1997, Schomig and Rau, 1995, van der Aalst, 1998, van der Aalst and ter Hofstede, 2000 and van Hee et al., 2000) since Zisman used PN to model workflow processes (Zisman, 1977). A petri net (PN) is a graphical and mathematical modeling tool. It consists of places, transitions, and arcs that connect them. Input arcs connect places with transitions, while output arcs start at a transition and end at a place. There are other types of arcs, e.g. inhibitor arcs. Places can contain tokens; the current state of the modeled system (the marking) is given by the number (and type if the tokens are distinguishable) of tokens in each place. Transitions are active components. They model activities which can occur (the transition fires), thus changing the state of the system (the marking of the petri net). Transitions are only allowed to fire if they are enabled, which means that all the preconditions for the activity must be fulfilled (there are enough tokens available in the input places). When the transition fires, it removes tokens from its input places and adds some at all of its output places. PN which model workflow process definition are called WF-nets (van der Aalst, 1998 and van der Aalst and van Hee, 1996). WF-nets are extended to MWF-nets with time, role, and resource information (Li et al., 2004). Methods are discussed to compute the workload that arrival transaction instances generate for the various resource pools and the lower bound of average turnaround time of transaction instances (Li et al., 2004). This paper adopts MWF-nets (Li et al., 2004) as a base mechanism to represent a performance analysis oriented workflow model.

This paper has presented a theoretical method to calculate the instances’ dwelling time probability density in a workflow where the activities are structured and predictable. By this method the instances’ dwelling time distribution and satisfactory degree based on dwelling time can be analyzed. An example has shown its availability in practice. This paper for the first time considers all the necessary information for the performance-related theoretical analysis of a workflow model. Firstly, an MWF-net is used to the model the workflow. Then, it is assumed that the service time of each resource agent is exponentially distributed and the instances arrive with exponentially distributed inter-arrival times. Since activities are the basic units of the workflow, the probability density function of instances’ dwelling time distribution in an activity is calculated firstly. Then with the result the functions in four control structures are computed. The method to obtain the function in a workflow is discussed. At last an approach is conducted to improve the dwelling time distribution of the instances. In this paper the routing of transaction instances in the TWF-net is mapped into the service request arrival rate. During the discussion of workflow performance-related analysis, it is assumed that service time of each resource agent is exponentially distributed and the instances arrive with exponentially distributed inter-arrival times and the resources do not need to repair. The techniques proposed in this paper need to be extended to deal with the case that service time and arrival interval are normally distributed and the resources have time to repair. This will be left for future exploration.