Traffic Source Models

In equation (2.16), the resource allocated to each data service queue consists of two parts of resource assignment. In the first part, the scheduler allocates the emergent queues, which queue occupancies are larger than queue length threshold, an amount of the difference between the queue occupancy and the queue length threshold. In addition, the longest queue has the highest priority to share the resource.

In second part, the scheduler allocates the remaining resource, denoted as R′, which is the available resource after allocation in the first part, as derived by equation (2.17), to each ONU again.

However, different from the first part, the allocation is based on the proportion of remaining queue occupancies.

The goal of first part is to avoid packets blocking, because the queue with larger queue occupancy has higher priority to be served. Thus, the first part is benefit to the fairness of packet blocking probability. In addition, the goal of second part is to avoid that all the resource is allocated to the greedy queues. So, the second part is benefit to the fairness of packet delay. As a result, by adopting the Hybrid LQF-QLP scheme, the fairness of packet delay and packet blocking probability can be considered simultaneously. It fits the original goal of scheduling the non-real-time service.

2.5 Simulation Result

2.5.1 Traffic Source Models

We consider three kinds of services, i.e. real-time voice, real-time video and best-effort data.

The priorities of these services are specified by P P₁, ₂, and ,P₃ where class P₁ service has the highest priority and class P₃ service has the lowest priority.

Class P₁ service is used to emulate a T1 connection. The packet generation rate of P₁ service is assumed to be the constant bit rate (CBR). The T1 data arriving from the user is packetized in the ONU by placing 24 bytes of data in a packet. By adding the overhead such as Ethernet, UDP (User Data Protocol) and IP (Internet Protocol) headers in a packet, the packet results in a 70-byte frame and would be generated every 125μs. Hence the data rate of class P₁ service is 4.48 Mbps.

Class P₂ service is used to emulate VBR video streams that exhibit properties of self-similarity and long-range-dependence (LRD). The packet size of this class of service is uniformly distribution and ranges from 64 to 1518 bytes. Class P₃ service has the lowest priority. It is used for non-real-time data transfer. The network does not guarantee the delivery or the delay of packets for this service. This class of service is also self-similar and LRD traffic with uniformly-distributed packet size ranged from 64 to 1518 bytes.

There is an extensive study, such as [17],[18],[19], and etc, showing that most network traffic flows can be characterized by self-similarity and long-range dependence (LRD). The characteristics of self-similar and LRD are described in Appendix A.

To generate self-similar traffic, we used the method described in [18], where the resulting traffic is an aggregation of multiple streams. The structure of the synthetic self-similar traffic generator is shown in Figure 2.8. Each source is performed by ON/OFF Parato-distributed model. The design of the number of sources (K) in a traffic generator is based on the experiment result discussed in [5]. It shows that the burstiness of the traffic (Hurst parameter) does not change with K if the total load is fixed.

Figure 2.8: Synthetic self-similar traffic generator

The traditional ON-OFF source models assume finite variance distributions for the sojourn time in ON and OFF periods. As a result, the aggregation of large number of such sources will not have significant correlation, except possibly in the short range. An extension to such traditional ON-OFF models allows the ON and OFF periods to have infinite variance (high variability or Noah Effect).

The superposition of many such sources produces aggregate traffic that exhibits long-range dependence (also called the Joseph Effect) [18].

Figure 2.9: ON/OFF Parato-distributed source i

Now we discuss the detail of each source. Figure 2.9 shows the model of source i. The parameters of this model are described as follows:

The number of packets generated by source i, denoted as Np_i, during ON period follows Pareto distribution with a minimum of 1 and maximum of 2¹⁶-1. Pareto distribution can be defined as follows: The choice of α was prompted by measurements on actual Ethernet traffic [19]. They reported the measured Hurst parameter of 0.8 for moderate network load. The relationship between the Hurst parameter and the shape parameter α is H = −(3 α) / 2 [18]. Thus, α =1.4 should result in

0.8 H = .

During ON period, the packet assumed to immediately follow the previous packet with minimum inter-packet gap t_g. We choose t_g equals to the standard preamble (8 bytes) of Ethernet packet.

Every source has a constant packet size from uniform distribution between 64 and 1518 (in bytes). We denote the packet size generated by source i is Ps_i. Then, the duration of ON period (tON) of source i can be described as

( ) bytetime ,

ON i g i

t = Ps +t ×Np × (2.20)

where bytetime depends on the line rate of EPON, i.e., bytetime = 8 / line rate.

OFF periods (intervals between the packet trains) also follow the Parato distribution with the shape parameter α =1.2. We used heavier tail for the distribution of the OFF periods represent a stable state in a network, i.e., a network can be in OFF state (no packet transmission) for an unlimitedly long time, while the durations of the ON Periods are ultimately limited by network

we must consider the average load we want to generate for this self-similar traffic generator. Suppose every source in traffic generator has the same parameters, then the average load, denoted as LOAD, can be represent as

According to equation (2.19), we know that

[ON] MIN_ON MIN_ON on_coef,

Then, the minimum value of OFF-period can be decided.

By aggregating streams from K independent sources, the realistic self-similar traffic is generated. We use the traffic generator to emulate two kinds of traffic sources, i.e., VBR video streams and best-effort data in our simulation.