در تجزیه و تحلیل عملکرد از ABR در شبکه های محلی ATM با شبکه های پتری تصادفی

In this paper we use Generalized Stochastic Petri Nets (GSPNs) and Stochastic Well-formed Nets (SWNs) for the performance analysis of Asynchronous Transfer Mode (ATM) Local Area Networks (LANs) that adopt the Available Bit Rate (ABR) service category in its Relative Rate Marking (RRM) version. We also consider a peculiar version of RRM ABR called Stop & Go ABR; this is a simplified ABR algorithm designed for the provision of best-effort services in low-cost ATM LANs, according to which sources can transmit only at two different cell rates, the Peak Cell Rate (PCR) and Minimum Cell Rate (MCR). Results obtained from the solution of GSPN models of simple ATM LAN setups comprising RRM or Stop & Go ABR users, as well as Unspecified Bit Rate (UBR) users, are first validated through detailed simulations, and then used to show that Stop & Go ABR is capable of providing good performance and fairness in a number of different LAN configurations. We also develop SWN models of homogeneous ABR LANs, that efficiently and automatically exploit system symmetries allowing the investigation of larger LAN configurations.

The UBR and ABR service categories (or transfer capabilities) standardized by the ATM Forum and the ITU-T [1] and [2] are considered the two main approaches for the provision of best-effort services in ATM networks. UBR stands for Unspecified Bit Rate; UBR provides very simple means for the transfer of the data resulting from best-effort services through ATM networks. The problem of UBR is that it can be quite inefficient, depending on the network configuration and load. ABR stands for Available Bit Rate; ABR provides flow control algorithms with variable degree of sophistication and efficiency to exploit the bandwidth not used by guaranteed-quality services for the transfer of the data resulting from best-effort services. The problem of ABR is that the flow control algorithms that permit good performance to be obtained are rather complex. Flow control in ABR is based on Resource Management (RM) cells that are periodically inserted within the flow of data cells along the connection; these RM cells travel from source to destination (forward RM cells), and then return to the source (backward RM cells). The ATM switches along the connection can use RM cells to notify sources about their congestion, and control the rate at which ABR sources inject cells into the network through feedback information. ABR sources are required to react to the feedback information by adequately modifying their cell transmission rates. Three ABR operating modes are specified; they define only the source behavior and the way the feedback is conveyed to sources, while the algorithm used in nodes to compute the feedback is not defined by standards. With Explicit Forward Congestion Indication (EFCI) ABR, just one bit of RM cells is used to convey to ABR sources the information about the congestion of the switches traversed by the connection (one bit in the header of data cells in the forward direction is also used with this operating mode). When sources receive RM cells with this bit set, they are required to reduce their cell transmission rate. With Relative Rate Marking (RRM) ABR, two bits of RM cells are used to instruct sources to reduce, to keep, or to increase their cell transmission rate. With Explicit Rate (ER) ABR, the congested switch along the connection path exactly instructs sources about the cell rate at which they are allowed to transmit (see for example [3] and [4]). In a recent paper [5] a simplified implementation of RRM ABR was proposed and named Stop & Go ABR, in which sources can transmit only at two different cell rates, the Peak Cell Rate (PCR) and Minimum Cell Rate (MCR). Detailed simulation results of simple Local Area Network (LAN) configurations were used to show that Stop & Go ABR is capable of providing performance and fairness practically identical to those of traditional RRM ABR algorithms, while allowing a simpler implementation within ATM switches, thus possibly leading to reduced cost of the ATM LAN equipment. Preliminary studies of the performance of ABR LANs with Generalized Stochastic Petri Net (GSPN) [6] and [7] models were presented in [8], considering the case of one ABR source. In this paper we further expand the performance analysis of ATM LANs with both RRM and Stop & Go ABR users in two ways: first we develop GSPN models of ATM LANs comprising ABR as well as UBR users, validating the results obtained from the solution of GSPN and SWN models through detailed simulations, and showing that Stop & Go ABR is capable of providing good performance and fairness in the considered LAN configurations. Second, we exploit system symmetries in case of homogeneous ABR sources by developing Stochastic Well-formed Nets (SWNs) [12] and [14] models to reduce the model state space and analyze larger systems.

The main contribution of this paper is in the development of detailed GSPN and SWN models for an ATM LAN with users exploiting the UBR and ABR ATM service categories (the latter in both the standard RRM version and the recently proposed Stop & Go version). To the best of the authors' knowledge, these are the first detailed Markovian models of the behavior of the ABR service category, that was thoroughly investigated by simulation and by different analytical approaches (see for example Chapter 4 in [18], and [19], [20] and [21]), and that is one of the prominent approaches for the provision of best-effort communication services within ATM networks. The adopted GSPN and SWN modeling approach is based on the use of just one timed transition that models the system clock, and numerous immediate transitions that describe the system operations. The exploitation of the model symmetries with SWNs in the case of homogeneous Stop & Go ABR sources allows remarkable savings in terms of the number of states to be considered in the model solution, and thus permits the analysis of ATM LANs with a larger number of users. Numerical results were obtained for several different ATM LAN configurations, and in a number of cases validated against very detailed simulation experiments, proving the accuracy of the GSPN and SWN modeling approach, and the effectiveness of the Stop & Go ABR algorithm in the considered LAN configurations.