A Novel Delay-Bounded Traffic Conditioner for
Optical Edge Switches
Vijay Sivaraman, David Moreland and Diethelm Ostry
ICT Centre, CSIRO
PO Box 76, Epping, NSW 1710, Australia
Email: {Vijay.Sivaraman, David.Moreland, Diet.Ostry}@csiro.au
Abstract— Optical Packet Switched (OPS) networks provide very lim-
ited contention resolution resources such as fibre delay lines (FDLs) and
wavelength converters. Effective use of these resources in minimising con-
tention losses within the all-optical core requires conditioning of traffic ag-
gregates by the optical edge switches. Traditional rate-based shapers such
as the leaky-bucket fail to provide acceptable delay performance for real-
time traffic aggregates; this paper therefore explores novel conditioning
mechanisms for OPS networks transporting traffic aggregates with time
constraints. Using as atheoretical basis a known off-line optimum smoother
for stored video traffic, we develop an on-line variable-rate conditioner that
approximates the off-line optimum, and requires O(1) amortised computa-
tion per packet arrival, making it amenable to efficient hardware imple-
mentation at the high data rates required by optical edge switches. We also
demonstrate via simulation of short and long range dependent traffic that
our conditioner allows losses in the optical core to be reduced by orders
of magnitude at the expense of a bounded and relatively low increase in
end-to-end delays. We believe that our conditioner can deliver significant
performance benefits when employed at the edge of an all-optical network.
Keywords: Optical Packet Switching, traffic smoothing
I. INTRODUCTION
Traffic burstiness is known to be detrimental to the perfor-
mance of any network. The situation is particularly acute in
optical packet switched (OPS) networks, where contention res-
olution resources such as fibre delay lines (FDLs) and wave-
length converters are used sparingly due to cost and size limita-
tions. Our previous work in [1], and similar studies in [2], have
shown that the conditioning of traffic at the ingress to the optical
network helps contain losses by allowing more effective utilisa-
tion of the sparse contention resolution resources. Conditioning,
however, incurs a cost, namely an increase in end-to-end delay
due to buffering at the conditioner. With traditional rate-based
shapers such as GCRA or leaky-bucket, this delay performance
is difficult to characterise, and requires assumptions about the
traffic model. With long range dependent (LRD) traffic that ex-
hibits burstiness at arbitrary time-scales, these shapers require a
high setting for the shaping rate, which renders the conditioning
ineffective in containing losses in the optical core.
Given the above inflexibility of rate-based shapers, we seek
a conditioner wherein the rate may be variable, but the delay
is bounded. The objective is, for arbitrary input traffic, to pro-
duce the smoothest output traffic that releases packets within
their time constraints. Smoothing has been studied extensively
in the context of video transmission. The authors in [3] con-
sider off-line smoothing of stored video, and establish a theo-
retical reference by identifying the optimal smoothing strategy
that minimises transmission rate variance subject to a given de-
lay bound and server/client buffer sizes. This has led to several
studies on dynamic smoothing of broadcast video streams [4],
[5], [6] (where a few seconds of distribution delay is accept-
able) as well as interactive video streams [7] (wherein only a
few frames can be buffered at the smoother).
This paper explores the use of delay-constrained traffic con-
ditioning in the context of optical networking. In contrast to
video applications where one or a few streams are smoothed at
end-hosts or video servers, optical networks require the smooth-
ing of traffic aggregates at very high data rates. We therefore
develop an online real-time conditioning algorithm that approx-
imates the off-line optimum and has constant amortised compu-
tational complexity per packet arrival. This makes it amenable
to efficient hardware implementation at high speeds. Unlike in-
teractive video smoothing techniques, our conditioner does not
predict or make assumptions about future arrivals, and is hence
traffic model independent. Using simulations of short and long
range dependent traffic, we show that our conditioner can re-
duce losses at a core OPS node by orders of magnitude, at the
expense of a few milliseconds of additional delay. We believe
our ideas can be very useful for future all-optical packet net-
works to provide acceptable loss performance without adversely
compromising end-to-end delays.
The rest of the paper is organised as follows. Section II
specifies the problem, and reviews the off-line optimality re-
sult from earlier work. In section III we propose a practical
real-time algorithm which approximates the off-line optimum,
and demonstrate its feasibility for implementation in practical
packet switches. Section IV demonstrates via simulation the ef-
fectiveness of our conditioning method in reducing burstiness,
and consequently losses at an optical core switch. Section V
summarises our contributions, and points out directions for fu-
ture study.
II. PROBLEM SPECIFICATION
The structure of the traffic conditioner we consider is shown
diagrammatically in figure 1. It consists of a FIFO queue, a
variable-rate server, and a rate controller which dynamically ad-
justs the server rate based on the deadline times τ
i
of packets
currently in the queue. The deadlines specify the times by which
each packet must have been placed on the output link. Packets
are assumed to enter the conditioner according to an arbitrary ar-
rival process and are released onto the output link by the server.
The limited buffering capability of contemporary optical
switch designs makes packet losses in an OPS core network
sensitive to burstiness in the traffic. Traffic burstiness can be re-
duced by a rate-based (e.g. leaky-bucket) shaping mechanism,
but this results in a traffic-dependent delay which may be unac-
ceptably large. In this work, therefore, we impose a constraint
2
τ
1
τ
τ
3
τ
n
rate
controller
input
output
server
service rate
Fig. 1. Traffic conditioner structure
τ
1
τ
2
τ
3
τ
k
0
T
delay bound
deadline curve
a feasible exit curve
arrival curve
Fig. 2. Arrival, deadline, and exit curves for an example workload process
that the delay experienced by a packet be no greater than some
prescribed bound d, and the goal of the rate controller in fig-
ure 1 is then to establish and maintain a service schedule which
gives the smoothest (i.e. least bursty) output traffic flow, while
ensuring that no packet exceeds its delay bound.
We briefly review previous work directed towards determin-
ing this service schedule. Consider the conditioner of figure
1 fed by an arbitrary input traffic stream. Suppose the system
starts at time 0 and stops at time T . Denote by A(t), 0 ≤ t ≤ T
the arrival curve, namely the cumulative workload that arrives
in the interval [0, t). The system starts empty, thus A(0) = 0.
Recall that traffic arriving at the conditioner has to be released
within the delay bound d; hence an arriving workload unit (i.e.
packet) at time t has deadline t + d. Denote by D(t), 0 ≤ t ≤ T
the deadline curve, namely the cumulative workload that has to
be served in [0, t) so as not to violate any deadlines. We set
D(0) = A(0) and D(T ) = A(T ). The curves A(t) and D(t)
are depicted in figure 2, and it can be observed that D(t) is a
right-shifted version of A(t) with a horizontal distance equal to
the delay bound d. Any service schedule can be represented by
a non-decreasing curve S(t), 0 ≤ t ≤ T describing a particular
cumulative exit curve. A feasible exit curve, that is, one which
is causal and satisfies the delay constraint, must lie in the region
bounded by the arrival curve A(t), and the deadline curve D (t).
Amongst all feasible exit curves, the one which corresponds
to the smoothest output traffic flow has been shown [3] to be
the shortest path between the origin and the point (T, A(T )),
as shown in figure 2. This curve always comprises a sequence
of straight-line segments joining points on the arrival and dead-
line curves, each segment representing a period during which
the service rate is a constant. Computation of this curve re-
quires knowledge of the complete traffic arrival curve, which
restricts the approach to off-line applications like the transmis-
sion of stored video files. Nevertheless the optimum exit curve
identified by this approach, (computed a posteriori in the case of
real-time flows) can provide a useful benchmark against which
to compare practical on-line algorithms.
The problem of determining good service schedules in on-
line applications has been studied in the context of transmitting
those video streams in which delays of seconds to minutes are
tolerable, for example in some news and sports broadcasts. The
framework provided by the optimum off-line schedule suggests
on-line algorithms which seek optimal schedules within a time
window maintained by introducing a delay buffer to implement
a lookahead capability (see for example [6]).
In this paper, however, we are concerned with the specific
goal of conditioning aggregated traffic at the ingress of optical
networks to compensate for severely limited buffer resources in
the network core switches. Traffic burstiness can cause losses
by overloading these resources, and our previous work [1] sug-
gests that such losses can be significantly reduced by smoothing
the traffic. The next section develops algorithms for real-time
conditioning of traffic within specified delay bounds.
III. A PRACTICAL ON-LINE TRAFFIC CONDITIONER
The off-line optimum identified above is useful in contexts
where the workload arrival is known in advance. At OPS edge
nodes, however, the packet arrival process is non-deterministic,
and the arrival curve is not known beforehand. We propose
an algorithm which is implementable in real-time, and approxi-
mates the off-line algorithm above. At any instant of time, our
on-line algorithm maintains the optimal (i.e. least bursty) exit
curve for the packets currently in the system, without account-
ing for future arrivals. Thus at time t, the arrival curve consid-
ered to the right of t is a horizontal line (since future arrivals
are not known yet), and the shortest-path exit curve degenerates
to the convex hull of the deadline curve. Upon each packet ar-
rival, the deadline curve is augmented, and this may require a
recomputation of the convex hull which defines the exit curve.
Figure 3 depicts the update algorithm performed upon each
packet arrival, and figure 4 illustrates the operations with an ex-
ample. Recalling that the convex hull is piecewise-linear, we
store it as a doubly linked list, where each element of the list cor-
responds to a linear segment whose start/end times and slope are
maintained. In step 1 of the algorithm, the length of the incom-
ing packet is determined, along with its deadline. The arrival of
this new packet causes the deadline curve to be amended, which
results in a new segment being appended to the hull. Steps 2-6
therefore create a new linear segment with the appropriate slope
and append it to the end of the hull (shown by operation a in
figure 4). The new piece may cause the hull to lose it convexity,
since the newly added piece may have slope larger than its pre-
ceding piece(s). Steps 7-11 therefore scan the hull backwards
and restore convexity. If a hull piece has slope larger than its
preceding piece, the two can be combined into a single piece
which joins the end-points of the two pieces (as depicted by op-
// determine length and deadline of newly arrived packet p
1. L = length(p); T = currtime; T
p
= T + d
// append new hull piece
2. h = new hullPiece
3. h.startT = ((hullList.empty()?) T : hullList.tail().endT);
4. h.endT = T
p
;
5. h.slope = L/(T
p
-h.startT)
6. hullList.append(h)
// scan backwards to restore hull convexity
7. h = hullList.tail()
8. while ((hPrev=h.prev)6=NULL ∧ hPrev.slope ≤ h.slope)
9. h.slope = [h.slope ∗ (h.endT − h.startT)
+ hPrev.slope ∗ (hPrev.endT − max(T, hPrev.startT))]
/ (h.endT − max(T, hPrev.startT))
10. hullList.delete(hPrev)
11. end while // the hull is now convex
Fig. 3. On-line algorithm for hull update upon packet arrival
B
A
packets
E
D
C
deadline curve
c
delay bound
time
packet arrival packet deadline
O
d
convexity holds at B; stop
replace C-D-E by C-E
convexity violated at D
convexity violated at C
replace B-C-E by B-E
new hull piece D-E
arrival
new packet
original hull: O-A-B-C-D
b
a
Final hull: O-A-B-E
Fig. 4. Illustration of hull update upon packet arrival
erations b and c in figure 4). The backward scan repeatedly
fuses hull pieces until the slope of the last piece is smaller than
the preceding piece (operation d in figure 4). At this stage the
hull is convex and the backward scan can stop, resulting in the
new convex hull.
We claim that the above algorithm, which needs to be per-
formed upon every packet arrival, has only O(1) amortised cost.
Claim 1: The algorithm of figure 3 has constant amortised
computation cost per packet arrival.
Proof: Our proof method follows a technique outlined for amor-
tised analysis in [8] that assigns a dollar cost to each unit of
computation. We start with the invariant that every point on the
hull has a $1 deposit associated with it. Upon packet arrival,
steps 1-6 are constant time operations, consuming $1 paid by
the arriving packet. Further, an additional $1 is deposited at the
end point of the newly added hull segment. The loop in steps
7-11 walks backwards through the hull checking for convexity
at each hull point. Each check is a constant time operation, and
is paid for by the $1 deposited at the hull point. If convexity
fails, the hull point is removed, fusing two hull pieces into one.
If convexity holds, the arriving packet deposits $1 at that hull
point, and the algorithm terminates. Thus each arriving packet
has paid a constant $3 in computation cost, and at termination
// for each slot
1. T = curTime; L = length(q.head())
2. credit = credit + hullList.head().slope
3. if (credit ≥ L)
4. dequeue and release packet
5. credit = credit - L
6. end if
// remove expired hull piece
7. if (hullList.head().endT ≤ T
8. delete hullList.head()
9. end if
Fig. 5. Service in each slot based on computed hull
of processing, a $1 deposit is still available at each hull point,
maintaining the invariant. This completes the proof. 2
In spite of a constant amortised cost per packet arrival, a
packet arrival in the worst-case may cause all hull points to
be scanned (steps 7-11) in order to restore convexity. In
those cases, practical implementations may choose from vari-
ous heuristics, such as limiting the backward scan to at most k
hull points, or restoring convexity every k-th packet arrival. The
study of these heuristics is deferred to future work.
The conditioner releases packets according to the computed
exit curve. This operation is straightforward, and is depicted for
a slotted OPS system in figure 5. Step 1 determines the current
slot time and the length of the packet at the head of the queue.
Steps 2-6 update the credit count based on the service rate in
the hull, and release the packet if sufficient credits are available,
while steps 7-9 remove the hull piece once it has been used and
pertains to the past. This sequence has O(1) complexity per slot.
We note that the hull computation algorithm does not constrain
the hull slope by the link rate. Since service rate cannot ex-
ceed link capacity, this can violate the delay bound d for some
packets. Though an implementation can choose to drop such
packets, we do not, for simplicity. Moreover, this allows us to
set the smoothing delay budget d = 0, which degenerates to the
unsmoothed case for comparison.
IV. SIMULATION STUDY
In this section we study the effectiveness of our proposed edge
conditioner in reducing burstiness of short and long range de-
pendent input traffic, and the corresponding impact on loss and
delay in a simple OPS network. The system is time-slotted, with
notional slot size of 1µsec, consistent with earlier works [9] and
current optical crossbar technology [10]. Each link operates at
10 Gbps per wavelength, and optical packets have fixed length
of 1250 bytes such that they fit exactly in one slot. Our generic
core switch is assumed to have a shared-memory architecture
[11] as shown in figure 6. No wavelength converters are em-
ployed, so each wavelength traverses its own switching plane.
Output port contentions are resolved using FDL buffers of ca-
pacity D, which denotes a set of FDLs of increasing length that
provide delays of 1, 2, . . . , D slots for all wavelengths. We sim-
ulate the simple network topology shown in figure 7, consisting
of eight edge nodes, each equipped with a conditioner, feeding
traffic into one core node having one output link. All our sim-
ulations assume a single wavelength, and load each input link
W
λ
1
λ
1
N
τ
τD
λ
2
(N+D) x (N+D)
Optical Crossbar
1
N
Switch Control Unit
Sync
Sync
pkt headers
Fig. 6. Generic core switch architecture
8x1 optical core switch
electro-optic
ingress edge switches
electro-optic
egress edge switch
optical cross-connect
FDLs
Fig. 7. Simulation topology
to 10% of link capacity; the output link is thus loaded at 80%.
Each simulation result corresponds to a run of at least 60 mil-
lion packets. Our burstiness measure β(s) corresponds to the
coefficient of variation of the traffic volume over time intervals
of length s. Log-log plots of β(s) versus s are routinely used to
indicate self-similarity of traffic traces and to show the influence
of the Hurst parameter H.
Our first simulation considers short-range dependent Pois-
son input traffic, whereby fixed-size optical packets at the edge
nodes have exponential inter-arrival times. Figure 8 plots bursti-
ness β(s) versus s on log scale for the input traffic stream, and
shows a straight line with slope −(1 − H) = −0.5 confirm-
ing H = 0.5 indicative of short-range dependent traffic. The
figure also plots the burstiness of the traffic released by the
conditioner, for smoothing delay bounds d of 1µsec, 10µsec,
100µsec, 1msec, and 10msec. The burstiness at time-scales of
one slot (i.e. log
2
s = 1) is invariant to conditioning, but as the
time-scale increases, smoothing significantly lowers burstiness
in comparison to the input traffic. As expected, the larger d is,
the smoother the traffic ouput by the conditioner. At time-scales
larger than d, the burstiness converges back to that of the input
stream, since smoothing ceases to be effective beyond the delay
0.0078125
0.015625
0.03125
0.0625
0.125
0.25
0.5
1
2
4
0 2 4 6 8 10 12 14 16
beta(s)
log_2(s)
input
d = 1usec
d = 10usec
d = 100usec
d = 1msec
d = 10msec
Fig. 8. Burstiness β(s) vs. time-scale log
2
(s) for Poisson traffic
10
0
10
1
10
2
10
3
0
5
10
15
20
25
30
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
smoothing delay (usec)
FDL buffer (usec)
aggregate pkt−loss
Fig. 9. Loss vs. edge smoothing delay and core FDL buffers for Poisson traffic
“window” d available to the conditioner. Since OPS networks
are expected to have small buffers, a relatively small d at the
edge conditioners should effectively lower burstiness at short
time-scales, helping reduce losses. Figure 9 plots the loss at the
core OPS switch, as a function of core FDL buffer capacity and
edge conditioning delay budget. Note first that if the OPS core
has no buffering, losses are invariant to smoothing, as predicted
by theory [1]. Also note that losses fall as FDL buffer capacity
increases, and also as the smoothing delay increases, showing
that our edge conditioning can substitute for core FDL buffering
in reducing losses in the OPS network. To achieve loss rates of
around 10
−4
in this example, one can choose to either equip the
core with 16µsec of buffering, or alternatively equip the core
with just 4µsec of buffering while employing our conditioner at
the edge nodes that introduce an additional delay bounded by
1msec. Since each µsec of FDL buffering translates to around
200 metres of fibre coil, the cost benefit of employing our edge
conditioners can be significant.
Our second scenario feeds each edge node with long range
dependent (LRD) traffic which has in recent years been shown
to be more representative of real traffic in data networks [12].
0.125
0.25
0.5
1
2
0 2 4 6 8 10 12 14 16
beta(s)
log_2(s)
input
d = 1usec
d = 10usec
d = 100usec
d = 1msec
d = 10msec
Fig. 10. Burstiness β(s) vs. time-scale log
2
(s) for LRD traffic
10
0
10
1
10
2
10
3
10
4
0
50
100
150
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
smoothing delay (usec)
FDL buffer (usec)
aggregate pkt−loss
Fig. 11. Loss vs. edge smoothing delay and core FDL buffers for LRD traffic
We generate LRD traffic using Norros’ self-similar traffic model
[13], with our filtering method developed in [14] that can gen-
erate very long sample paths of fractional Gaussian noise. We
set the Hurst parameter H = 0.85, and the average link loads
are as in the previous case. Figure 10 plots the burstiness β(s)
versus s on log scale for the input traffic, and the slope of
−(1 − H) = −0.15 validates the Hurst parameter setting of
0.85 (the different slope at lower time-scales is explained by the
discretization of the ideal fluid model required to generate pack-
ets). The figure also shows burstiness of the ouput produced by
our conditioner with delay budget d of 1µsec, 10µsec, 100µsec,
1msec, and 10msec. Once again our conditioner is very effective
in reducing burstiness up to time-scales corresponding with the
conditioner delay budget. Figure 11 shows how this translates
into loss performance at the OPS core node, as the FDL buffer
capacity and edge conditioner delay budget are varied. Note first
that in the absence of conditioning (smoothing delay budget of
10
0
= 1 slot), the losses fall off sub-exponentially (following a
power-law) as the FDL buffer capacity increases. This is typical
for LDR traffic, and signifies that the incremental cost of FDLs
required to reduce the loss by a desired amount gets progres-
sively higher. Now observe that increasing the conditioner delay
budget reduces losses, though the fall is slower than for Poisson
traffic. In the absence of conditioning, loss rates of around 10
−4
in this example require FDL buffer capacity of 80µsec at the
core, whereas with conditioners that add only 1msec of delay,
the required FDL buffer capacity is no more than 16µsec, which
translates to a substantial savings in cost. These results indicate
that our conditioner is effective for both short- and long-range
dependent input traffic.
V. SUMMARY
This paper investigated the use of traffic conditioning at the
optical edge to reduce contention losses in core optical packet
switched (OPS) networks with very limited buffering. We ex-
plored novel conditioning mechanisms derived from known off-
line optimum smoothing techniques for stored video traffic.
We presented an on-line real-time conditioner that has constant
amortised computational cost per packet arrival, and is imple-
mentable at the high data rates required by optical edge nodes.
Via simulation, we demonstrated the efficacy of our conditioner
in reducing burstiness and losses at an OPS core node for both
short and long range dependent traffic input, which translates
into significant cost savings in the design of OPS networks.
Our future work targets extensions of the above conditioner
to include multiple traffic classes with distinct delay require-
ments. We are also working on quantifying the benefits accruing
from the use of our conditioner in more extensive OPS network
topologies.
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