Modeling mobile agent behavior

g e y w o r d s M o b i l e agents, Dwell time, Life span, Report statistics, Behavior. 1. I N T R O D U C T I O N Mobile agents are self-executable programs tha t t ravel a round a network doing work [1]. The ana ly t ica l model ing and solution of models of mobile agent behavior is in its infancy. This paper presents fundamenta l analyt ica l models to i l lus t ra te the rich s t ruc ture of the mobile agent paradigm. Our intent is not to propose one model to "fit all" s i tua t ions but to exhibi t a number of compl imenta ry models tha t indicate the model ing possibi l i t ies of mobile agents. The probabl is t ic assumpt ions have been kept general, phrasing l ifet ime resul ts in te rms of Laplace t ransforms and expectat ions. However, more sophis t ica ted model ing and analysis is cer ta inly possible bu t is beyond the scope of this paper which is to suggest a foundat ion for further e laborat ion. Mobile agents have numerous appl icat ions but their appl icab i l i ty to networking and telecommunicat ions is of par t icular interest . In this context , mobile agents can be used for collecting, d a t a mining [1], and processing network management informat ion [2-4] as well as delegat ing network control in networks. Mobile agents can move around a network based on a specific rout ing plan [5] and t r anspor t a mobile agent 's s ta te , code, and d a t a [6] to perform these functions. For instance, in a large network such as the In ternet or a te lephone network, a mobile agent(s) can be dispatched to problemat ic network nodes to invest igate node s t a tus ra ther than dumping all nodal s tatus , s ta t is t ics and configurat ion informat ion to a network control center. In addit ion, The support of NSF grant CCR-9912331 in the course of T. Robertazzi's research is gratefully acknowledged. 0898-1221/06/$ see front matter (~) 2006 Elsevier Ltd. All rights reserved. Typeset by A ~ T E X doi: 10.1016/j.camwa.2005.11.030 952 S.-H. KIM AND T. G. ROBERTAZZI if a mobile agent finds a problem based on the information collected, it can take action such as redirecting traffic. Thus, the use of mobile agents can reduce network traffic and provide an intriguing means of implementing functionality. In some cases, a node can dispatch a mobile agent(s) before it starts to transmit its traffic to determine the network status. Based on collected network information by the mobile agent, a node can decide on an optimal path. Mobile agent modeling must take into account a number of novel behaviors. These include the fact that mobile agents reside in a host for some time (dwell time), have a finite lifespan, can make copies of themselves (cloning), be discarded (killed), report results to a central station, and may have to deployed in sufficient numbers to carry out a task according to some specification (quality of service). All of these quantities can be statistically described in various ways. An understanding of these issues is necessary for designing optimal mobile agents codes, and network parameters (such as host speed and network capacity). There is very little work to date on analytical stochastic modeling of mobile agent behavior. Mobile agents can be represented by stochastic Petri nets [7-11], which are usually solved numerically. However, our interest is primarily in analytical models of mobile agent behavior. To this end, we present a conceptual framework showing that common mobile agent functions can be analytically described in terms of stochastic models. Note that it is not our intention to present definitive distributional models of mobile agent behavior (this awaits experimental work). We indicate below where assumptions are made for the sake of providing examples. The true significance of this paper is in demonstrating the power and possibilities of analytical stochastic models of agent behavior. Note also that analytical mobile agent stochastic modeling is related to the theory of branching processes [12]. This paper is organized as follows. Section 2 describes mobile agent functions. Section 3 covers dwell time distributions. Modeling mobile agent life span is discussed in Section 4. The interreport process of a mobile agent is examined in Section 5 and mobile agent report arrival processes are studied in Section 6. Section 7 discusses an optimization problem involving the minimum number of mobile agents needed to provide a desired quality of service level. Finally, the conclusion appears in Section 8. 2. M O B I L E A G E N T F U N C T I O N S Mobile agent functions can be categorized into three major groups which are a network management function [1], a secretary function [6], and a maintenance function [13]. A secretary function (user level) allows a user/customer to command a mobile agent that does a specific job within a given time and with the best result or performance. A network management function (network level) lets a mobile agent travel around the network to collect network information, or allows a mobile agent to be delegated responsibility by the network controller. Finally, a maintenance function (connection level) helps to maintain connection/call and data transport. Figure I depicts the difference among three mobile agent application levels. The details of network, connection and user level are explained in [14]. The information reporting mechanism is an important factor in deciding the performance of mobile agents as well as that of networks. The reporting characteristics (i.e., interreporting) analysis of mobile agents can be divided into two categories depending on the number of reports to a central node or control node. The two categories are persistent reporting and intermittent reporting. Persistent reporting means that a mobile agent reports from every node it visits. Examples of persistent reporting include the network management function and the maintenance function. For the case of the network management function, a mobile agent travels around the network, collects information and reports the network's current state successively. The maintenance function may have to track an object's movement involving a cellular communication customer or data file transfer, thus causing many reports to be generated. In intermittent reporting, a mobile agent Modeling Mobile Agent Behavior I~ Computers Laplop computer Mobile Agents Mobile Terminals Figure 1. Different mobile agent application levels. IZ 953 reports from some of the nodes it visits. The secretary function is an example of intermittent reporting. The secretary function may reside in a host or a market place which is composed of many hosts, and a mobile agent reports when it achieves its goal. Thus, the number of reports for the network management function and the maintenance function is generally larger than for the secretary function. 3. D W E L L T I M E D I S T R I B U T I O N One or more mobile agents may be inserted into a network from a central host (network center) for management purpose and each resides in different hosts for periods of time. The dwell (or residence) time in a host is an important parameter that influences information reporting behavior. During the residence of mobile agents that travel from host to host, mobile agents make measurements and report results back to the central host. If a mobile agent arrives at a host, the processor in a host will act pre-emptively for mobile agents because it is assumed that every mobile agent has the highest priority and must be served without delay (queueing delay could be included). The dwell (or residing) time of a mobile agent in a host, D is D = Execution time + Reporting time. (i) One cycle time, C is C = D + Travel (or Propagation) time to next host. (2) Figure 2 illustrates the cycle of execution time, reporting time and travel (or propagation) time to an adjacent host. Dwell time depends on the network host status, specifically, congestion, job load in a host, and processor speed, etc. Here, the time periods are assumed to be independent of each other. During execution time, the mobile agent may sojourn in a host 's microprocessor and collects host status information. It may include some type of network center delegation processes, such as rerouting traffic, or reconfiguring the node. Reporting time contains such latency as execution suspension, data serialization, encoding [6], report generation to the source and report propagation delay and acknowledgment delay from the source. The report round trip propagation delay 954 S.-H. KIM AND T. G. ROBERTAZZI Reporting State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .