Tài liệu Giới thiệu về IP và ATM - Thiết kế và hiệu suất P15 ppt

CHARACTERIZING AN AGGREGATE OF PACKET FLOWS In the previous chapter, we assumed that the arrival process of packets could be described by a Poisson distribution which we modified slightl

15 Resource Reservation

go with the flow

QUALITY OF SERVICE AND TRAFFIC AGGREGATION

In recent years there have been many different proposals (such as Inte-grated Services [15.1], Differentiated Services [15.2], and RSVP [15.3]) for adding quality of service (QoS) support to the current best-effort mode of operation in IP networks In order to provide guaranteed QoS, a network must be able to anticipate traffic demands, assess its ability to supply the necessary resources, and act either to accept or reject these demands for service This means that users must state their communications require-ments in advance, in some sort of service request mechanism The details

of the various proposals are outside the scope of this book, but in this chapter we analyse the key queueing behaviours and performance characteristics underlying the resource assessment

To be able to predict the impact of new demands on resources, the network needs to record state information Connection-orientated tech-nologies such as ATM record per-connection information in the network

as ‘hard’ state This information must be explicitly created for the duration

of the connection, and removed when no longer needed An alternative approach (adopted in RSVP) is ‘soft’ state, where per-flow information is valid for a pre-defined time interval, after which it needs to be ‘refreshed’

or, if not, it lapses

Both approaches, though, face the challenge of scalability Per-flow

or per-connection behaviour relates to individual customer needs With millions of customers, each one initiating many connections or flows,

it is important that the network can handle these efficiently, whilst still providing guaranteed QoS This is where traffic aggregation comes in ATM technology introduces the concept of the virtual path – a bundle of virtual channels whose cells are forwarded on the basis of their VPI value

Second Edition J M Pitts, J A Schormans Copyright © 2000 John Wiley & Sons Ltd ISBNs: 0-471-49187-X (Hardback); 0-470-84166-4 (Electronic)

only In IP, packets are classified into behaviour aggregates, identified by

a field in the IP header, and forwarded and queued on the basis of the value of that field

In this chapter, we concentrate on characterizing these traffic aggre-gates, and analysing their impact on the network to give acceptable QoS for the end users Indeed, our approach divides into these two stages: aggregation, and analysis (using the excess-rate analysis from Chapter 9)

CHARACTERIZING AN AGGREGATE OF PACKET FLOWS

In the previous chapter, we assumed that the arrival process of packets could be described by a Poisson distribution (which we modified slightly,

to derive accurate results for both M/D/1 and M/G/1 queueing systems) This assumption allowed for multiple packets, from different input ports,

to arrive simultaneously (i.e within one packet service time) at an output port, and hence require buffering This is a valid assumption when the input and output ports are of the same speed (bit-rate) and there is no correlation between successive arrivals on an input port

However, if the input ports are substantially slower than the output port (e.g in a typical access multiplexing scenario), or packets arrive in bursts at a rate slower than that allowed by the input port rate (within the core network), then the Poisson assumption is less valid Why? Well, suppose that the output port rate is 1000 packet/s and the traffic on the input port is limited to 100 packet/s (either because of a physical bit-rate limit, or because of the packet scheduling at the previous router) The minimum time between arrivals from any single input port is then

10 ms, during which time the output port could serve up to 10 packets The Poisson assumption allows for arrivals during any of the 10 packet service times, but the actual input process does not

So, we characterize these packet flows as having a mean duration, T on,

and an arrival rate when active, h (packet/s) Thus each flow comprises

the rate of flows arriving is simply

We can interpret this arrival process in terms of erlangs of offered traffic:

offered traffic D Ap

i.e the flow attempt rate multiplied by the mean flow duration

1 2

P I

P I input ports

Output port

of interest

Figure 15.1. Access Multiplexor or Core Router

It may be that there is a limit on the number of input ports, P I, sending flows to the particular output port of interest (see Figure 15.1) In this case, the two scenarios (access multiplexor, or core router/switch) differ

in terms of the maximum number of flows, N, at the output port For the access multiplexor, with slow speed input ports of rate h packet/s, the

maximum number of simultaneous flows is

N D PI However, for the core router with input port speeds of C packet/s, the

maximum possible number of simultaneous flows it can support is

C h



i.e each input port can carry multiple flows, each of rate h, which have

been multiplexed together upstream of this router

PERFORMANCE ANALYSIS OF AGGREGATE PACKET FLOWS

The first task is to simplify the traffic model, comprising N input sources,

to one in which there is a single aggregate input process to the buffer (see Figure 15.2), thus reducing the state space from 2Npossible states to just

2 This aggregate process is either in an ON state, in which the input rate exceeds the output rate, or in an OFF state, when the input rate is not zero, but is less than the output rate

For the aggregate process, the mean rate in the ON state is denoted

Ron , and in the OFF state is R off When the aggregate process is in the ON

state, the total input rate exceeds the service rate, C, of the output port,

and the buffer fills:

rate of increase D R onC

N−1

N−2

1

2 state process

…

2N state process

Exponentially distributed ON period Exponentially distributed OFF period

Ron

Roff

Figure 15.2. State Space Reduction for Aggregate Traffic Process

The average duration of this period of increase is denoted T
on To be

in the ON state, more than C/h sources must be active Otherwise the

aggregate process is in the OFF state This is illustrated in Figure 15.3

In the OFF state, the total input rate is less than the service rate of the output port, so, allowing the buffer to empty,

rate of decrease D C  R off

The average duration of this period of decrease is denoted T
off.

Reducing the system in this manner has obvious attractions; however, just having a simplifying proposal does not lead directly to the model in detail Specifically, we need to find values for the four parameters in our two-state model, a process which is called ‘parameterization’

S

1 2 3

C/h -1 C/h

.

.

Channel capacity = C

ON period

OFF period

ON period T(on) = mean ON time Ron = mean ON rate

OFF period T(off) = mean OFF time Roff = mean OFF rate

Figure 15.3. Two-State Model of Aggregate Packet Flows

Parameterizing the two-state aggregate process

Consider the left-hand side of Figure 15.3 Here we show the combined input rates, depending on how many packet flows are active The capacity

assigned to this traffic aggregate is C packet/s – this may be the total

capacity of the output port, or just a fraction if there is, for example, a

weighted fair queue scheduling scheme in operation If C/h packet flows

are active, then the input and output rates of the queue are equal, and the queue size remains constant From the burst-scale point of view, the queue is constant, although there will be small-scale fluctuations due to the precise timing of packet arrival and departure instants If more packet flows are active, the queue increases in size because of the excess rate; with fewer packet flows active, the queue decreases

in size

Let us now view the queueing system from the point of view of the

arrival and departure of packet flows The maximum number of packet

flows that can be served simultaneously is

h

We can therefore think of the output port as having N0 servers and a buffer for packet flows which are waiting to be served If we can find the mean number waiting to be served, given that there are some waiting,

we can then calculate the mean rate in the ON state, R on, as well as the

mean duration in the ON state, T
on.

Assuming a memoryless process for the arrival of packet flows (a reasonable assumption, since flows are typically triggered by user activity), this situation is then equivalent to the system modelled by Erlang’s waiting-call analysis Packet flows are equivalent to calls, the

output port is equivalent to N0circuits, and we assume infinite waiting space The offered traffic, in terms of packet flows, is given by

Erlang’s waiting-call formula gives the probability of a call (packet flow) being delayed as

D D



Ð











N01

rD0





or, alternatively, in terms of Erlang’s loss probability, B, we have

The mean number of calls (packet flows) waiting, averaged over all calls,

is given by

But what we need is the mean number waiting, conditioned on there being some waiting This is simply given by

w

A

Thus, when the aggregate traffic is in the ON state, i.e there are some packet flows ‘waiting’, then the mean input rate to the output port exceeds the service rate This excess rate is simply the product of the conditional

mean number waiting and the packet rate of a packet flow, h So

Ap

C  Ap

The mean duration in the excess-rate (ON) state is the same as the conditional mean delay for calls in the waiting-call system From Little’s formula, we have

which, on rearranging and substituting for w, gives

Ton

A

So, the conditional mean delay is

Ton

h Ð Ton

C  Ap

This completes the parameterization of the ON state In order to

para-meterize the OFF state we need to make use of D, the probability that a

packet flow is delayed This probability is, in fact, the probability that the

aggregate process is in the ON state, which is the long-run proportion of time in the ON state So we can write

T
on

which, after rearranging, gives

D

The mean load, in packet/s, is the weighted sum of the rates in the ON and OFF states, i.e

and so

1  D

Analysing the queueing behaviour

We have now aggregated the Poisson arrival process of packet flows into a two-state ON–OFF process This is very similar to the ON–OFF source model in the discrete fluid-flow approach presented in Chapter 9, except that the OFF state now has a non-zero arrival rate associated with

it In the ON state, we assume that there are a geometrically distributed number of excess-rate packet arrivals In the OFF state, we assume that there are a geometrically distributed number of free periods in which

to serve excess-rate packets Thus the geometric parameters a and s are

given by

and

For a finite buffer size of X, we had the following results from Chapter 9:

and

The state probabilities, p
k, form a geometric progression which can be

written as

p
k D









a s

Ðp
0 0 < k < X



s

1  a

 Ð



a s

These state probabilities must sum to 1, and so, after some rearrangement,

we can find p
0 thus:

p
0 D

1 a

s

1 



1  s

1  a

 Ð



a s

Now, although we have assumed a finite buffer capacity of X packets for this excess-rate analysis, let us now assume X ! 1 The term in the denominator for p
0 tends to 1, and so the state probabilities can be

written

p
k D



1 a

s

 Ð



a s

As we found in the previous chapter for this form of expression, the

probability that the queue exceeds k packets is then a geometric

progres-sion, i.e

Q
k D



a s

This result is equivalent to the burst-scale delay factor – it is the

proba-bility that excess-rate packets see more than k in the queue It is in our,

now familiar, decay rate form, and provides an excellent approximation

to the probability that a finite buffer of length k overflows This latter is a

good approximation to the loss probability

However, we have not quite finished We now need an expression for

the probability that a packet is an excess-rate arrival In the discrete fluid-flow model of Chapter 9, this was simply
R  C/R – the proportion of

arrivals that are excess-rate arrivals This simple expression needs to be modified because when the aggregate process is in the OFF state, packets are still arriving at the queue

We need to find the ratio of the mean excess rate to the mean arrival rate If we consider a single ON–OFF cycle of the aggregate model, then this ratio is the mean number of excess packets in an ON period to the

mean number of packets arriving in the ON–OFF cycle Thus

Prfpacket is excess-rate arrivalg D
RonC Ð T
on

which, after substituting for R on , T
on and T
off , gives

Prfpacket is excess-rate arrivalg D h Ð D

C  Ap

The queue overflow probability is then given by the expression

















xC1

VOICE-OVER-IP, REVISITED

In the last chapter we looked at the excess-rate M/D/1 analysis as

a suitable model for voice-over-IP The assumption of a deterministic server is reasonable, given that voice packets tend to be of fixed size,

and the Poisson arrival process is a good limit for N CBR sources when

N is large (as we found in Chapter 8) But if the voice sources are using

activity detection, then they do not send packets during silent periods Thus we have ON–OFF behaviour, which can be viewed as a series of overlapping packet flows (see Figure 15.1)

Suppose we have N D 100 packet voice sources, each producing packets

at a rate of h D 167 packet/s, when active, into a buffer of size X D 100 packets and service capacity C D 7302.5 packet/s The mean time when active is T onD0.35 seconds and when inactive is T off D0.65 second, thus

each source has, on average, one active period every T onCToff D1 second

The rate at which these active periods arrive, from the population of N

packet sources, is then

TonCToff D100 s

1

Therefore, we can find the overall mean load, A p, and the offered traffic,

A, in erlangs.

A D F Ð TonD100 ð 0.35 D 35 erlangs

and the maximum number of sources that can be served simultaneously, without exceeding the buffer’s service rate is

h D43.728 which needs to be rounded down to the nearest integer, i.e N0D43 Let’s now parameterize the two-state excess-rate model

B D

N0

rD0

r!

D0.028 14

We can now calculate the geometric parameters, a and s, and hence the

decay rate

decay rate D a

s D0.964 86

The probability that a packet is an excess-rate arrival is then

Prfpacket is excess-rate arrivalg D h Ð D

and the packet loss probability is estimated by



a s

D4.161 35 ð 104

Figure 15.4 shows these analytical results on a graph of Q
x against x The

Mathcad code to generate the analytical results is shown in Figure 15.5 Also shown, as a dashed line in Figure 15.4, are the results of applying the burst-scale analysis (both loss and delay factors, from Chapter 9) to the same scenario Simulation results for this scenario show a decay rate

of approximately 0.97 The figure of 0.964 86 obtained from the excess-rate aggregate flow analysis is very close to these simulation results, and illustrates the accuracy of the excess-rate technique In contrast, the burst-scale delay factor gives a decay rate of 0.998 59 This latter is typical

of other published techniques which tend to overestimate the decay rate

by a significant margin; the interested reader is referred to [15.4] for a more comprehensive comparison

If we return to the M/D/1 scenario, where we assume that the voice sources are of a constant rate, how many sources can be supported over the same buffer, and with the same packet loss probability? The excess-rate analysis gives us the following equation:

Q
100 D



 Ðee2C Ce

 1 C e

D4.161 35 ð 104

0 10 20 30 40 50 60 70 80 90 100

Buffer capacity, X

10 0

10−1

10−2

10−3

10−4

10−5

Figure 15.4. Packet Loss Probability Estimate for Voice Sources, Based on Excess-Rate Aggregate Flow Analysis