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A High Performance Channel Sorting Scheduling
Algorithm Based On Largest Packet
P.G.Sarigiannidis, G.I.Papadimitriou, Senior Member, IEEE and A.S.Pomportsis
Department of Informatics, Aristotle University, Box 888, 54124 Thessaloniki, Greece
Abstract-We present a new algorithm for wavelength division
multiplexing (WDM) star optical networks. The resulting
protocol is pre-transmission coordination-based without
packet collisions. The proposed algorithm tries to schedule
the transmission requests of the network, with the assistant
of a prediction mechanism. With the prediction of the packet
requests the algorithm manages to decrease the calculation
time of building the schedule matrix, which consists of the
final schedule of the packets of each node of the network.
This reduction is achieved by pipelining the computation
process, at the same time with the adoption of a new order in
which nodes` requests are serviced. This modification of the
service order leads to an increment in terms of network
throughput and channel utilization. We compare the
performance of two algorithms in terms of channel
utilization, network throughput and mean time delay, under
different sets of channel values and we present the
simulation results.
I. INTRODUCTION
The today existence of the electronic switching speeds
cannot satisfy the constantly increasing demands for high
speed within local area networks (LAN), metropolitan
area networks (MAN), and wide are networks (WAN).
Photonic networks are expanding rapidly, due to the
enormous bandwidth of optical fiber technology [1].
Wavelength division multiplexing (WDM) technology
transports tens to hundreds of wavelengths per fiber, with
each wavelength modulated at 10 Gb/s or more. Such
systems may result in gigabit-per-second data rates in
independent channels, which transmit simultaneously data
flows to a single or multiple users [2]. In this paper, we
focus on WDM LANs, based on broadcast and select (BS)
architecture. More specifically, in this context the network
consists of a number of nodes, a set of channels, and a
passive (or physical) star coupler [3]. At a given time
every node can select an available channel in order to
transmit its data to the appropriate destination. The
transmission comes through by the passive star, which
broadcasts all input data to all outputs and allows
transparent and immediate transfer of data from the
transmitters to the receivers.
Node 0
Node 1
Node N-1
Pathetic Star
Receiver
W Transmitters Array
Receiver
W Transmitters Array
Receiver
W Transmitters Array
.
.
.
Figure 1. The network model
We consider data transmission in a single-hop WDM
optical network whose nodes are connected to a passive
star coupler via a two way fiber (Fig. 1). The network
comprises N nodes and W channels. Each node disposes
an array of tunable transmitters, which provides the
transmission of data to the appropriate channels. With this
approach the channels are pre-allocated to the nodes.
Moreover, the node has a fixed receiver, which allows
receiving data in the particular channel, which is
dedicated to each node, known also as home channel. A
home channel may be shared if the number of nodes
exceeds the number of channels within network [2]. Thus,
the network is multicasting and unicasting. The
connection of the channels is accomplished through the
passive star coupler.
A medium access control (MAC) protocol manages to
allocate the available channels to the nodes, which are
ready to transmit to a specific destination. In order to
export conclusions for the functionality of a MAC
protocol, we should investigate the two types of collisions
that are possible to occur in WDM BS networks [4].
Firstly, a channel collision occurs when two or more
nodes try to transmit within the same wavelength
simultaneously. Secondly, a receiver collision occurs
when two or more nodes try to transmit the data
simultaneously to the same node in different wavelengths.
Undoubtedly, such a case is possible only in architectures
with tunable receivers.
MAC protocols are generally categorized as either pre-
transmission co-ordination based or pre-allocation [4]. In
the case where in the network there is at least one channel
dedicated to the coordination of channels and their
transmission time, then the protocol is based on pre-
transmission coordination. In a different case, i.e., if the
network does not make use of a separate channel for the
node transmission control, the protocol is pre-allocation
based. Undoubtedly, at many instances it is observed that
protocols do not dispose a separate control channel but
exert control through control packets. We suppose that the
time is divided in time frames. Each frame is composed of
a reservation phase and a transmission phase. Also, each
frame consists of a number of timeslots, during which the
reservation and the packet transmission take place. In pre-
transmission co-ordination based protocols the algorithm
accepts the time demands of each node of the network and
stores them in a transmission frame, called traffic demand
matrix, D=[di,j]. The traffic demand matrix show off the
load of the network.
II. BACKGROUND
A very important scheduling algorithm of pre-
transmission coordination based networks is online
interval-based scheduling (OIS) [5]. OIS is an online
algorithm and that means that begins schedule
computation just after reading the requests of the first
node. So the algorithm needs only a part of the demand
matrix to function. That has the advantage to save
schedule computation time, because starts to build the
schedule matrix, before the total acceptance of the nodes’
demands.
It is important to refer that OIS starts to operate once a
set of requests by node n is known. Let us suppose that the
node n demands t1 timeslots to accomplish the
transmission, via channel w1. OIS searches for availability
between timeslot t and timeslot t + (t1-1). If during this
time gap node n is not engaged to any other channel w1
(w≠w1) then the coordination is accomplished and the
time gap t to t + (t1-1) is registered to node n, with channel
w. In the next step OIS refresh the lists and examines the
remaining demands of the rest N-1 nodes of the network.
In this way, every timeslots within the final schedule
matrix of OIS contains a registration of transmission by a
specific node via a specific channel. Of course if there are
no registered nodes for some specifics spaces in the
schedule matrix the equivalent channel stays idle and the
time gap unused.
A notable continuation of OIS is predictive online
scheduling algorithm (POSA) [6]. Its aim is to extend and
improve OIS, by decreasing the computation time of the
scheduling matrix. This is accomplished with the aim of
hidden Markov chains, which allows to algorithm to
predict the demands of the nodes for the next frame. In the
same time POSA transmits the data of the current time.
This parallel action leads to a significant time saving,
since the algorithm does not lose time, by waiting the
delivery of the node’s demands. In addition, constructs the
scheduling matrix immediately, based on the prediction,
made during the previous frame. It is clear that such a
prediction is based on the real requests of the nodes.
POSA collects these requests from the passed frames and
stores them into history queues. POSA uses two different
algorithms. In the beginning of each frame POSA runs the
learning algorithm and collects and informs its history
queues about the new demands. After the learning
algorithm POSA apply the second algorithm, known as
prediction algorithm. This part of POSA is responsible for
the prediction of the following frame. Thus during the
prediction algorithm POSA tries to predict the demands of
the frame which follows.
III. FM-POSA
The proposed new protocol is called first max-
predictive online scheduling algorithm (FM-POSA). The
first part of the name (FM) is an acronym related to the
operation of the scheduling algorithm while the second
part (POSA) states that the proposed algorithm is based on
POSA which it evolves and improves [6]. The algorithm
operates in three independent phases, the learning phase,
the shifting phase and the prediction phase. In the first
phase, the algorithm monitors the network traffic and tries
to learn about the variations in traffic. The algorithm also
updates the history queues about the changes in traffic so
that it can make accurate predictions later. In the second
phase the algorithm stops monitoring and updating and
enters the prediction phase. Finally, in the last and most
important phase the algorithm predicts the nodes’ requests
for the next frame based on its learning phase. In addition
the algorithm performs the forwarding of packets to their
destinations.
The new element that is introduced by FM-POSA is the
order in which the nodes’ requests are processed. It is easy
to see that POSA process the nodes’ requests one after the
after (serially) starting from the first node and finishing
with the last one. This means that POSA does not examine
the size or the behavior of the nodes in detail but always
processes the requests in the same order. FM-POSA on
the other hand records and compares the nodes requests
based on a key point i.e. the largest packet size. Thus,
FM-POSA searches for the largest packet and sorts nodes
according to this. The first node that is served is the one
with the largest packet following by the one with the
second largest packet and ending with the one with the
smallest packet. It is worth to mention that if two nodes
have packets of equal size the node that will be served
first is randomly selected.
It would be useful to see an example of the processing
of a demand matrix in order to understand the operation of
both algorithms. Consider the following demand matrix:
D =
1..4..6
3..3..2
1..2..2
. We must remind you that the rows in this
table are the network nodes and the columns are the
network channels. It is obvious that in this table that we
study we have nine independent predictors where every
one of them predicts for a node-channel pair. With the
above data, predictor p0,0 has predicted that node N0 will
require two timeslots for the scheduling of packets to their
destinations using channel W0. The same logic stands for
all other predictors until the last one p2,2 which predicts
one timeslot for channel W2 and N2.
Given this demand matrix the OIS and POSA algorithms
would construct a scheduling matrix, which the service of
requests starts from the first node N0 and continues with
node N1 and finishes with node N2. On the other hand,
FM-POSA operates gradually in two actions:
Action 1: Search and locate the largest packet from the
requests of the nodes and save it in a vector called MAX.
By executing this action FM-POSA forms the following
vector MAX. MAX =
6
3
2
. By observing the vector
MAX, it is easy to see that the longest request for node N0
is equal to two timeslots, for node N1 three timeslots and
for node N3 six timeslots.
Action 2: Reorder the elements in MAX in descending
order.
By executing this action FM-POSA forms the final vector
S_MAX: S_MAX =
2
3
6
The reordering of vector MAX means that the processing
of requests in order to produce the scheduling matrix is
dictated by the final vector S_MAX. In other words the
first node that is processed is the one with the longest
request in timeslots, i.e. node N2 with 6 timeslots, the
second node that is processed is node N1 and the last one
is node N0.
In this context let us examine the final form of the
schedule matrix, constructed by POSA-OIS and FM-
POSA. Given the demand matrix D of the above example
the final schedule matrix, constructed by POSA will be as
this in Figure 1.
timeslots
012345678910
N0N2
Wo
W1
N0N1
N0
N1
N0N1
N2N2N2N2N2
N1
N2
idle
idle
idle
idle
W2N2
idle
idle
N0
N1
idle
N1
N1N1
idle
idle
idle
idle
idle
11
N2
idle
idle
N2
idle
idle
12 13
N2
idle
idle
Figure 2. The final schedule matrix, constructed by POSA
It is easy to observe that POSA spends a total 14 timeslots
to finalize the schedule matrix. Also, POSA wastes a total
18 idle sub-timeslots. So POSA losses a 43% percent of
matrix’s cells:
43.0
...3*......14
......18 =
channelstimeslotsoverall
tssubtimesloidle
In contrary FM-POSA will construct the following
schedule matrix (Fig. 2):
timeslots
012345678910
N2
N1
N1
Wo
W1
N2N2
N1N1
N2
N0N0
N2N2N1N0N0
N2
N2
idle
idle
idleidle
W2N0
idle
idle
N1N1
idle
N2N2N2
idleidle
N1
Figure 3. The final schedule matrix, constructed by FM-POSA
If we examine the schedule matrix of Figure 3, we will
notice that FM-POSA starts to construct the matrix, by
processing the requests of N2. Then the algorithm
continues with N1’s requests and completed the
construction with N0’s requests. This service order
shifting leads to an evident gain, in terms of timeslots,
which can be translated in real time. FM-POSA spends a
total of 11 timeslots, and concurrently wastes only 9 idle
subtimeslots. Hence, FM-POSA losses only 27% percent
of matrix’s cells:
27.0
...3*......11
......9 =
channelstimeslotsoverall
tssubtimesloidle
IV. SIMULATION RESULTS
This section presents the simulation results of the two
algorithms POSA and FM-POSA. The two algorithms
have been studied in the terms of utilization, network
throughput and mean time delay, under uniform traffic.
We consider two network models. The first consists of 4
channels and a row of nodes (10, 20, 30, 40, and 50). The
second consists of 8 channels and a row of nodes (10, 20,
30, 40, and 50). It is important to refer that N symbols the
number of nodes, W symbols the number of channels, K
is the maximum value for incoming packets. Also, it is
important to pinpoint that the speed of the line has been
defined at 2.4 Gbps. The tuning latency is considered to
be equal to zero for simplicity reasons. The duration of the
simulation is 10000 frames, from which 1000 belongs to
learning phase and the rest to the prediction phase. Finally,
K is not constant but equal to FLOOR(NW/5).
The results from the comparison between the two
algorithms in terms of channel utilization proves that FM-
POSA remains constantly better that POSA, either for 4 or
for 8 channels (Figures 4, 5). The results from the
comparison between the two algorithms in terms of
throughput proves that FM-POSA remains again
constantly better that POSA, either for 4 or for 8 channels
(Figures 6, 7). Lastly, the results from the comparison
between the two algorithms in terms of throughput vs.
delay shows that as the time delay is increased FM-POSA
precedes POSA. Concurrently, FM-POSA presents a
lower mean time delay than POSA, for each value of the
workload (Figures 8, 9).
Figure 4. Channel Utilization with 4 channels
Figure 5. Network Throughput with 4 channels
Figure 6. Throughout vs. Delay with 4 channels
Figure 7. Channel Utilization with 8 channels
Figure 8. Network Throughput with 8 channels
Figure 9. Throughput vs. Delay with 8 channels
V. CONCLUSIONS
In this paper we introduced a new scheduling algorithm
for collision free WDM star networks. The new scheme
offers a better utilization of the available channels of the
network and brings an improvement in channels
utilization and network throughput by changing the order
of the processing of each node based on the largest
request.
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] K. M. Sivalingam, K. Bogineni, and P. W. Dowd, “Pre-allocation
media access control protocols for multiple access WDM photonic
networks”, ACM SIGCOMM Computer Communication, vol. 22,
no. 4, 1992, pp. 235-246.
[3] C.A. Brackett, “Dense wavelength division multiplexing network:
Principles and applications”, IEEE J. Selected Areas Commun., vol.
8, 1990, pp. 948-964.
[4] G. I. Papadimitriou, P. A. Tsimoulas, M. S. Obaidat and A. S.
Pomportsis: Multiwavelength Optical LANs, Wiley, 2003.
[5] 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, (January 2002),
pp. 73-87.
[6] 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, (July
2001), pp. 271-286.
Channel Utilization (W=4)
70%
75%
80%
85%
90%
95%
10 20 30 40 50
Nodes
Utilization (%)
POSA FM-POSA
Throughput vs. Delay (W=4)
0
100
200
300
400
500
600
700
800
7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0
Throughput (Gpbs)
Mean Time Delay (timeslots)
POSA FM-POSA
Channel Utilization (W=8)
55%
60%
65%
70%
75%
80%
85%
10 20 30 40 50
Nodes
Utilization
POSA FM-POSA
Network Throughput (W=4)
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
10 20 30 40 50
Nodes
Throughput (Gbps)
POSA FM-POSA
Network Throughput (W=8)
11
12
13
14
15
16
17
10 20 30 40 50
Nodes
Throughput (Gbps)
POSA FM-POSA
Throughput vs. Delay (W=8)
0
100
200
300
400
500
600
700
800
11 12 13 14 15 16 17
Throughput (Gbps)
Mean Time Delay (timeslots)
POSA FM-POSA
