Content uploaded by Panagiotis G. Sarigiannidis
Author content
All content in this area was uploaded by Panagiotis G. Sarigiannidis
Content may be subject to copyright.
12th Annual Symposium of the IEEE/CVT, Nov. 3, 2005, Enschede, the Netherlands 1
WFF: A High Performance Scheduling Algorithm for
WDM Star Networks that Minimizes Idle Timeslots
P.G.Sarigiannidis, G.I.Papadimitriou, Senior Member, IEEE, and A.S.Pomportsis
Department of Informatics, Aristotle University, Box 888, 54124 Thessaloniki, Greece
A new media-access control (MAC) protocol is introduced in this paper. We consider a
Wavelength Division Multiplexing (WDM) network with star topology. The protocol
adopted is pre-transmission coordination-based, so the protocol coordinates nodes
before the actual transmission. The protocol introduces a new method of computing the
reservations of the demand matrix and brings some performance improvement, which is
proven by simulations in terms of channel utilization, throughput and delay.
Introduction
If we suppose that the main advantage of optical switching is that it enables routing of
optical data signals without the need for conversion to electrical signals then we can
easily understand that it is the key factor of the future networks [1]. The WDM
technique [2,3] brings this to reality by dividing the available optical bandwidth into
multiple channels of lower bandwidth, which can be easily supported by the nodes’
electronic circuits. The absence of the optical to electronic form conversion [4] offers
Gigabit data rates; hence the multiplexing and the demultiplexing of the available
channels (or wavelengths) are performed optically.
WDM Broadcast-and-Select star Networks belong to the WDM networks family
and achieve a considerably high performance [5], using a passive star coupler in order
to route all transmitted data from its inputs to its outputs. The presented protocol
assumes a WDM broadcast-and-select LAN (Local Area Network) with N nodes and W
wavelengths.
Each node is equipped with an
array of W fixed transmitters (or a
tunable transmitter); hence each node
can transmits using any channel.
Also, a fixed receiver allows each
node to receive in a particular
channel, knows as its home channel
(Fig. 1). Data transmission occurs
sequentially in data frames, which are
divided further in timeslots. In each
frame the protocol examines the
transmission requests of the network
nodes and performs schedule
processing in order to specify the order
in which nodes will transmit in each
channel. There is no restriction in the
number of nodes that can transmit in each frame. Every node can send its transmission
requests and have them assigned to a timeslot. In addition, every node has access to
every transmission channel. However, there are two things that cannot be realized. First,
Fig.1. Broadcast and Select star network with
tunable transmitter and fixed receiver per node. The
network has N nodes and W channels.
N
od 0
N
od 1
N
ode -1
Passive Star
Receiver
W Transmitters Array
Receiver
W Transmitters Array
Receiver
W Transmitters Array
.
.
.
12th Annual Symposium of the IEEE/CVT, Nov. 3, 2005, Enschede, the Netherlands 2
a node cannot transmit simultaneously in two channels and second, two or more nodes
cannot transmit simultaneously using the same channel.
Online Algorithms
As a typical online scheduling algorithm, OIS (online interval scheduling) [6] shares the
advantage of online algorithms in that it does not require that the entire demand matrix
becomes available before it begins schedule computation. Instead, OIS begins
constructing the transmission schedule as soon as the requests of the first node are
available. OIS functions as follows: assume that node n requests t
1
timeslots for
transmission in channel w and that OIS determines that there is a time period in the next
frame during which the requested channel is available i.e. there exists a value t such that
the channel is available from timeslot t to timeslot t + (t
1
- 1). Next, OIS examines the
possibility of contentions. If the algorithm concludes that the scheduled transmission
does not result in any collisions, it includes it in the scheduling matrix that is being
constructed. As a result, at any given timeslot the request table (scheduling matrix) of
OIS comprises of the nodes that are scheduled to transmit and the wavelengths they will
transmit in.
In order to decrease the delay that a ready node experiences while waiting for OIS
to compute the schedule, POSA (predictive online scheduling algorithm) [7] attempts to
minimize the duration of the schedule computation process by predicting the nodes’
requests for the next frame. In this direction POSA makes use of a hidden Markov chain
and attempts to predict the requests of the nodes for the subsequent frame based on their
requests for the previous frame. Because the algorithm does not wait for the nodes to
send their requests in order to compute the schedule but starts working based on the
predictions, a significant amount of time is saved.
WFF algorithm
In this section we present a scheme called Wait For Fullness (WFF), that is based on the
two previous algorithms that were discussed namely OIS [6] and POSA [7]. This new
protocol attempts a synthesis of the main features of OIS and POSA and results in a
performance improvement in terms of channel utilization and network throughput. WFF
introduces a new schedule computation mechanism called the cleanup mechanism. The
innovation of WFF lies in the way it modifies the scheduling algorithm so that it
minimizes (or even eliminates) the number of idle timeslots thus significantly
improving channel utilization while maintaining a high network throughput. WFF
incorporates the same prediction mechanism as POSA which when combined with the
pipelining of the schedule computation time and transmission time explains the
significant performance improvement that is observed.
The innovative cleanup mechanism of WFF acts on the scheduling matrix. It is
actually a procedure during which the timeslots that contain at least one idle channel are
located and logically erased so that the total number of idle timeslots is minimized and
the channel utilization is increased. The function of the cleaning mechanism can be
divided into the following four steps:
1. Locate the timeslots that contain at least one idle channel (referred to as idle
timeslots).
2. Logically erase these timeslots and construct the scheduling matrix without these
timeslots.
12th Annual Symposium of the IEEE/CVT, Nov. 3, 2005, Enschede, the Netherlands 3
3. Reschedule the requests that were contained in the
deleted timeslots.
4. At regular predetermined intervals perform the refresh
function and schedule all stored (in queues) packets so
as to put an upper bound on the incurred service
delay.
The discovery of idle timeslots is a pretty simple
procedure. After constructing the scheduling matrix
according to OIS or POSA, the lines of the matrix
(corresponding to channels) are scanned one by one for all columns (i.e. for all
timeslots). When a slot containing at least one idle channel is located it is logically
erased which means that the transmissions it contains will be performed in one of the
following frames. This means
that the requests that were
rescheduled will be added to the
new requests that the nodes will
send for the following frame
and the actual data will continue
to be stored in queues while
their transmission is being
scheduled.
It is obvious that if the
algorithm always functioned
according to the cleanup
mechanism the channel
utilization would be
approximately equal to 100%
since the number of idle slots
would be almost zero. This
ideal level of channel utilization
and the corresponding high
network throughput come at the
cost of a significant delay since
the number of packets waiting
in queues constantly increases
and their scheduling is referred
for later. For this reason the
cleaning mechanism includes a
process called refresh function
during which the contents of the
waiting queues are emptied (all
waiting packets are scheduled
for transmission). This refresh
function is performed at regular
frame intervals (i.e. every time a
constant number of frames have
elapsed). For the frame that the
Table 1. Scheduling matrix contructed by OIS or POSA
timeslots
01234567891011
N0
N1
N2
wo
w1
N0 N0
N3 N3
N1
N0 N0
N1 N1 N1 N2 N3
N2 N2 N2
i
d
le
i
d
le
i
d
l
e
i
d
l
e
i
d
le
i
d
le
timeslots
01234567891011
N0
N1
N2
wo
w1
N0 N0
N3 N3
N1
N0 N0
N1 N1 N1 N2 N3
N2 N2 N2
i
d
l
e
i
d
l
e
i
d
l
e
i
d
l
e
i
d
l
e
i
d
l
e
Table 2. Identification of idle timeslots
12345
N0 N0
N3 N3
N1
N0 N0
N1
N3
N2
0
N0
N1
wo
w1
timeslots
Table 3. The final sheduling matrix
after step 2 of cleanup mechanism
D
f
=
2..1
3..2
1..4
2..3
, D`
f
=
0..0
2..2
0..2
0..0
Frame 1. Demand matrixes
for frame f
12th Annual Symposium of the IEEE/CVT, Nov. 3, 2005, Enschede, the Netherlands 4
refresh function is performed, WFF functions as OIS or POSA, and the specific frame is
named as refresh frame.
The function of the cleanup mechanism is clarified with an example. Consider a
network with 4 nodes (N
0
, N
1
, N
2
and N
3
) that transmit data using two channels (W
0
and
W
1
). Assume that a total of 18 requests are submitted for frame f and that these requests
are distributed, where D
f
is the demand matrix for frame f (Frame 1.). From the matrix,
it is evident that node N
0
requests three timeslots for channel W
0
and two timeslots for
channel W
1
, node N
1
requests four timeslots for channel W
0
and one timeslot for
channel W
1
, node Ν
2
requests two timeslots for channel W
0
and three timeslots for
channel W
1
and node Ν
3
requests one timeslot for channel W
0
and two timeslots for
channel W
1
.
The application of OIS or POSA would result in the scheduling matrix of Table 1.
At this point the cleanup mechanism is activated. The timeslots that include at least one
idle channel are identified. These timeslots are 5, 6, 7, 8, 10, and 11 (Table 2.). The
second step of the cleanup mechanism is to exclude these timeslots (or equivalently the
corresponding transmission requests) from the scheduling matrix. This results in the
scheduling matrix of Table 3. It must be pointed out that the requests included in the
deleted timeslots are not overlooked. The third step
of the cleanup mechanism is the rescheduling of
these requests in the frame that follows (together
with the nodes’ actual requests for the next frame).
Therefore two timeslots for node N
1
and two
timeslots for node N
2
in channel W
0
and two
timeslots for node N
2
in channel W
1
will be
rescheduled. The new demand matrix that contains
the cumulative nodes’ requests for frame f+1,
denoted as D`
f
is shown in Frame 1. Summarizing
the schedules computed for frame f, it can be observed that the schedule length for OIS
and POSA is equal to 12 timeslots while the schedule length for WFF is merely 6
timeslots. The number of idle slots for OIS and POSA is equal to 6 while there are
naturally no idle timeslots for WFF.
Assume that the demand matrix D
f+1
for the next frame (i.e., frame f+1) is as
shown in Frame 2. According to the cleanup mechanism the demand matrix for frame
f+1 would be the result of the addition of tables D`
f
+D
f+1
. Therefore the new demand
matrix for frame f+1 would be equal to
D`
f
+D
f+1
=
0..0
2..2
0..2
0..0
+
6..2
0..4
2..1
3..3
=
6..2
2..6
2..3
3..3
In this particular case, if we construct the scheduling matrix we will observe that
contains only one timeslot with an idle channel. The rescheduled requests are contained
in D`
f+1
(Frame 2.). In conclusion, for frame f+1, OIS and POSA construct a schedule of
16 timeslots while the schedule constructed by WFF has duration of 13 timeslots. There
are no idle slots for WFF in contrast to OIS and POSA where the number of idle
timeslots is 11.
D
f+1
=
6..2
0..4
2..1
3..3
, D`
f+1
=
0..0
0..0
0..0
0..1
Frame 2. Demand matrixes for
frame f+1
12th Annual Symposium of the IEEE/CVT, Nov. 3, 2005, Enschede, the Netherlands 5
We complete our example by considering a last set of demands D
f+2
for frame f+2
(Frame 3.) According to the cleanup mechanism the demand matrix for frame f+2
would be the result of the addition of tables D`
f+1
+D
f+2
. Therefore the new demand
matrix would be equal to:
D`
f+1
+ D
f+2
=
0..0
0..0
0..0
0..1
+
1..3
4..2
1..3
2..4
=
1..3
4..2
1..3
2..5
If we assume that refresh function is performed during
frame f+2 we can draw some important conclusions from this
example. The total number of nodes’ requests for frames f to f+2
is equal to 59 (18 for the first frame, 21 for the second frame and
20 for the third). In order to service these requests OIS/POSA
utilize a total of 41 timeslots (12 in frame f, 16 in frame f+1 and
13 in frame f+2) while WFF utilized a mere 32 timeslots (6 in
frame f, 13 in frame f+1 and 13 in frame f+2). The total number
of wasted timeslots for OIS/POSA is 23 while WFF only wasted
5 timeslots (all in the last frame when cleaning reset is
performed).
Simulation results
In the results of the simulation, it is assumed that N is the number of nodes; W is the
number of the channels and K is the maximum value over all entries in the traffic
matrix. POSA and WFF have been studied and analyzed under uniform traffic. The
speed of the line has been defined at 2.4 Gbps. The metric, called refresh rate, means
how often refresh function is executed. For example if refresh is equal to 2, then two
normal frames is followed by one refresh frame.
The results from the comparison between POSA and WFF, in terms of channel
utilization are shown in Figure 2 for two channels and in Figure 3 for three channels.
It is obvious that WFF remains constantly better than POSA for each number of nodes,
either for 2 or for 3 channels. The results from the comparison between the two
algorithms in terms of throughput are shown in Figure 4 for two channels and in Figure
5 for three channels.
Fig.2. Channel Utilization (W = 2)
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
10 20 30 40 50 60 70 80 90 100
Nodes
Utilization %
POSA
WFF (refresh = 2)
WFF (refresh = 4)
Fig.3. Channel Utilization (W = 3)
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
10 20 30 40 50 60 70 80 90 100
Nodes
Utilization %
POSA
WFF (refresh = 2)
WFF (refresh = 4)
D
f+2
=
1..3
4..2
1..3
2..4
Frame 3. Demand
matrix for frame
f+2
12th Annual Symposium of the IEEE/CVT, Nov. 3, 2005, Enschede, the Netherlands 6
The results from the comparison between the two algorithms in terms of
throughput vs. delay are presented in the Figure 6 for two channels and Figure 7 for
three channels. It is obvious that for each value of the workload, WFF precedes POSA
without a significant time delay.
Conclusions
This paper presented an improved protocol for WDM Broadcast-and-Select networks,
which minimizes idle timeslots. The protocol eliminates the collisions by coordinating
the demands of the nodes before the transmission with the help of a cleanup mechanism.
According to simulation results it improves not only the schedule utilization and the
throughput of the network, but also the mean time delay in relation to the throughput.
References
[1] G. I. Papadimitriou, Ch. Papazoglou, and A. S. Pompotrsis, “Optical Switching : Switch Fabrics, Techniques,
and Architectures”, IEEE/OSA Journal of Lightwave Technology, vol. 21, no. 2, 2003, pp. 384-405.
[2] C.A. Brackett, “Dense wavelength division multiplexing network: Principles and applications”, IEEE J.
Selected Areas Commun., vol. 8, 1990, pp. 948-964.
[3] T. E. Stern, and K. Bala, Multiwavelength Optical Networks, Addison-Wesley, 1999.
[4] P. Green, “Progress in optical networking, IEEE Communications magazine”, vol. 39, no. 1, 2001, pp. 54-61.
[5] G. I. Papadimitriou, P. A. Tsimoulas, M. S. Obaidat, and A. S. Pomportsis, Multiwavelength Optical LANs,
Wiley, 2003.
[6] K. M. Sivalingam, J. Wang, J. Wu and M. Mishra, “An interval-based scheduling algorithm for optical WDM
star networks”, Photonic Network Communications, vol. 4, no. 1, 2002, pp. 73-87.
[7] E. Johnson, M. Mishra, and K. M. Sivalingam, “Scheduling in optical WDM networks using hidden Markov
chain based traffic prediction, Photonic Network Communications”, vol. 3, no. 3, 2001, pp. 271-286.
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
10 20 30 40 50 60 70 80 90 100
Nodes
Throughput in Gbps
POSA
WFF (refresh = 2)
WFF (refresh = 4)
Fig.4. Network Throughput (W = 2)
5.5
5.7
5.9
6.1
6.3
6.5
6.7
6.9
7.1
7.3
10 20 30 40 50 60 70 80 90 100
Nodes
Throughput in Gbps
POSA
WFF (refresh = 2)
WFF (refresh = 4)
Fig.5. Network Throughput (W = 3)
0
100
200
300
400
500
600
700
13.3 13.4 13.6 13.7 13.9 14.0 14.2 14.3
Throughput in Gbps
Mean Time Delay in timeslots
POSA
WFF (refresh = 2)
WFF (refresh = 4)
0
100
200
300
400
500
600
700
12.5 12.7 12.9 13.1 13.3 13.5 13.7 13.9 14.1 14.3
Throughput in Gbps
Mean Time Delay in timeslots
POSA
WFF (refresh = 2)
WFF (refresh = 4)
Fig.7. Throughput vs. Mean Time Delay (W = 3) Fig.6. Throughput vs. Mean Time Delay (W = 2)
