Performance analysis of the p_i-persistent protocol in unidirectional bus networks

Abstract

The p_i-persistent medium access protocol is an attractive solution for high-speed time-slotted unidirectional bus networks. This protocol, with its very simple flow control mechanism allowing station i to access empty slots with station-dependent probability p_i, has been seen as an alternative for solving fairness problems associated with the original IEEE 802.6 standard for the distributed queue dual bus (DQDB) for high-speed networks. In this paper we analyze the main aspects of the fairness provision mechanism employed in the p_i-persistent protocol. Assuming heavy traffic load, the stations' access probabilities are determined so as to allocate certain portions of the channel capacity for guaranteeing prescribed service requirements. Having determined the probability generating function of queue length as well as the two first moments of the worst-case packet delay (delay of the last packet arriving at a station within a slot time) for a single station, we investigate packet delays and fairness in a bus network with N stations. Our results show that, in a network with homogeneous Poissonian arrival streams, if the bus is able to carry all the offered load, protecting fairness of services by lowering the access probability at a station leads only to deterioration of that station's performance without affecting performance of other stations. This is a surprising result which however does not apply for bursty traffic, as shown by the results of our simulation studies.

Introduction

In a series of papers Mukherjee et al. 1, 2, 3, 4, 5 proposed a medium access protocol for high-speed time-slotted unidirectional bus networks, known as the p_i-persistent protocol. This is a straight adoption of the well-known p-persistent protocol of broadcast busses (cf. [6]), in which stations linked by unidirectional (folded or dual) busses have different station-dependent probabilities of accessing empty slots. The p_i-persistent protocol, with its very simple flow control mechanism, has been seen as an alternative for solving fairness problems associated with the original IEEE 802.6 standard for the distributed queue dual bus (DQDB) for high-speed networks 7, 8, 9, 10, 11. Conceptually similar techniques, based on accessing slots according to station-dependent priorities, had been earlier considered in [12] for single and in 13, 14 for multiple unidirectional busses.

Protocols of this type are based on open loop flow control schemes and can be attractive in high-speed networks since in such networks, even in the case of a folded bus, feedback information in the upstream direction is not available in a timely manner. Various alternative solutions for medium access control (MAC) protocols in slotted unidirectional busses, including those implemented in CRMA, Fasnet and Hangman networks, can be found surveyed e.g. in [15].

Under the p_i-persistent protocol each slot is able to carry one data packet of fixed size plus some overhead bits necessary for synchronization and control of the network. If station i has a packet to send, it persists with its attempt to transmit the packet in the next free slot with probability p_i (see Fig. 1). The closer a station is located to the origin of the bus the larger is the probability that it encounters a free slot. If, as an extreme case, station 1 always has packets to transmit and its access probability per slot is 1, then there will be no free slots available for subsequent stations.

Packet delays under the p_i-persistent protocol have been investigated in [16] by modeling contents of subsequent slots as a two state switched Bernoulli process. By matching corresponding moments an approximate analysis is carried out for any number of coupled stations. The exact upper and lower bounds on the average packet delay and queue length for the original p_i-persistent protocol and its deterministic counterpart, in which station i can access only each ⌈1/p_i⌉ empty slot, are given in [17]. If the access probabilities are properly selected, the rate of accessing the channel by different stations can be balanced.

In a network with N stations the probabilities p_i, 1≤i≤N, can be chosen also adaptively by sensing the actual load on the bus. Corresponding methods have been suggested by [3]. Besides flexibility concerning load changes, this also allows for dynamic integration of new stations. After a short sensing period, where an appropriate access probability p_i is estimated, new stations simply use empty slots for transmission. However, this induces a certain management overhead, particularly if the whole network is reconfigured. This price has to be paid to achieve fair network access, independent of the position on the bus.

Reference [5] deals with fairness of the p_i-persistent protocol by introducing different criteria, e.g. equal mean packet delay, equal blocking, and equal throughput. It is assumed that each station has equal finite buffer capacity M to store packets, arriving at station i according to a Poisson process with intensity λ_i. If an arriving packet encounters a filled buffer, it is blocked and lost. Of course, if high blocking rates are tolerated, low delay times are easily achievable, for instance by reducing the buffer size. To compromise these two criteria is the most critical issue of the protocol. The network and the access bridges should be designed in such a way as to cope with the major part of the entire traffic load, which is also stressed in [1].

It is obvious that mechanisms used for enforcing fairness in communication networks can potentially worsen their performance. Thus, detailed studies of tradeoffs between fairness and efficiency of different networks are needed. The main purpose of this paper is to investigate the relationship between the fairness enforcement mechanism and performance of a network operating under the p_i-persistent protocol. Pursuing this goal we look at the network from an operator's point of view, and assume that a certain guaranteed capacity of the network is bought by clients, just enough to satisfy their individual needs. If there is extra unused capacity available, it is offered to all subscribers in order to improve their throughput and delay times. New subscribers receive their ordered capacity, hence the possibility that others' quality of service will be reduced, but never below the guaranteed threshold. A network control of this type can be implemented by dynamically steering the access probabilities p_i, which offers an elegant way of warding off overload.

A surprising point emerges from the case when the bus is able to carry all offered traffic from Poisson arrival streams, or more generally, from (non-batched) arrival processes with independent increments. Then, if an active upstream station i reduces its access probability p_i to allow fairer treatment of downstream stations, this deteriorates the waiting times at station i, but does not improve waiting times at subsequent stations i+1,…,N. Hence, fairness can be achieved only by sacrificing a certain part of overall performance.

We set out to describe briefly the topology of the bus which was basically developed in [5]. Empty slots are generated by a control station, and slots drop off the bus at the end (black boxes in Fig. 1). N stations are using the bus for communication by sensing the outbound and inbound bus channel. Stations are labeled 1,…, N according to their relative position on the bus, starting with the station closest to the control station. The packet arrival stream at station i is assumed to be a process with independent increments with mean λ_i (packets per slot), where packets arrive entirely at time instants, e.g. in bulks of 64 bits in parallel. Packets are sequentially copied bit-by-bit to the channel. To simplify the analysis we assume that each station has an infinite buffer to store locally generated packets. If a station has a packet to send, it independently attempts to transmit it in the next slot with probability p_i, provided this slot is empty. With probability 1−p_i it leaves an empty slot, which is passed for use by subsequent stations. We furthermore suppose that the arrival processes at different stations are stochastically independent.

A new packet arriving at a random instant τ at a buffer already filled with k packets has to wait a random number of slots until the k packets ahead are cleared. Moreover it has to wait a random number of slots until its own transmission starts, and one slot until it is completely copied to the channel, counted from the beginning of the next slot after its arrival time τ (see Fig. 2). Hence, the minimum waiting time for a packet arriving at an empty buffer is 1.

The basic problem now is how to choose the p_i such that the above-described requirements apply. We start by analyzing the queue length and packet delay at each station and their dependence on the access probabilities.