Sigmoid Function Based Dynamic Threshold Scheme for Shared-Buffer Switches Boran Gazi†, Zabih Ghassemlooy‡
†
Electronics Research Group, Sheffield Hallam University, Sheffield, Phone: +44(0)114 225 3254, Fax: +44(0)114 225 3433, Email:
[email protected] ‡ Optical Communications Research Group, University of Northumbria, Newcastle, Phone: +44(0)191 227 4902, Email:
[email protected]
Abstract – Buffer space in packet switching nodes is an important network resource. Shared buffer switches are prone to high packet losses and unfair use of buffer space. The use of a buffer management scheme is necessary to overcome these problems. This paper investigates the performance of Sigmoid Function Threshold scheme by means of simulations. This scheme regulates the usage of shared buffer space by employing multiple thresholds for packet admission. The results show that it performs well under non-uniform input traffic; nevertheless buffer space reserved for lightly loaded output ports is wasted due to the strict packet admission control. Keywords: Dynamic buffer management, shared buffer switch.
I. Introduction
environment parameters. As expected, dynamic policies outperform static policies as they are more aware of network dynamics (e.g. traffic load and pattern, link failure, priority traffic etc). Push out (PO) or drop on demand (DoD) is known as the best policy as it is fair, efficient and naturally
adaptive
implementation
is
[2]. almost
However impossible.
practical Newly
developed policies aim to achieve the same performance as DoD with low implementation overhead. Dynamic threshold (DT) is developed to achieve the dynamism of DoD together with simplicity of static threshold (ST) [3]. Another policy, maximum busy period (MBP), developed by Sharma and Viniotis, aims to keep output ports as busy as possible by simply pushing out a packet from the
An important issue of the overall control in
queue with the highest busy period [4]. Finally,
communication networks is the management of
adaptive fuzzy threshold scheme uses fuzzy rules and
buffers at the packet switching/routing nodes.
membership functions to set the threshold according
Various studies have shown that shared buffer switch
to the overall occupancy of the shared buffer [5]. The
(SBS) is better than other buffering schemes in terms
main drawback is that the parameters of the
of packet loss performance [1]. It provides a notion
membership functions have to be set and tuned
of flexibility when allocating space for contending
through various simulations.
packets. Note that SBS greatly suffers from
The aim of this paper is to adapt the Sigmoid
inefficient use of buffer space (e.g. packet loss rate,
function based fuzzy threshold policy [6] (developed
fairness) when network traffic is bursty and
for single server queue, M/D/1) to SBS; and contrast
asymmetric [1].
its performance to well-known DT. Section II
A buffer management policy can be adapted for
provides a brief explanation of both DT and Sigmoid
efficient and effective use of buffer space in SBSs.
Function Threshold (SFT) schemes. Simulation
There have been many attempts in the literature to
model is presented in Section III and simulation
tackle this problem [1][2][3]. These policies can be
results are discussed in Section IV.
mainly categorised into two main classes: Static and dynamic policies. The first one is based on static
II. Dynamic Buffer Management
parameters set based on statistical information and
A. Dynamic Threshold (Choudhury & Hahne) DT scheme sets a single queue threshold for all
the latter attempts to control the common buffer space based on the information from dynamic
of the dynamic length queues on the basis of the amount of empty buffer space. Purpose of this
scheme is to spare some space for unutilised output
III. Simulation Model
ports in order to prevent fully utilised output ports
In order to measure the performance and
from dominating the usage of buffer. Simply, a
understand the characteristics of both of the schemes,
packet is rejected if the queue length of that port
a program is developed by using parallel virtual
exceeds the threshold value at time t, T(t) [3]:
machine (PVM) platform. The aim of using this
T (t ) = α .( M − Q(t ))
(1)
platform is to achieve a realistic environment with asynchronous and independent working processes
Where M is the total buffer capacity, Q(t) the amount
(traffic generators, queue controller, and buffer
of buffer space occupied at time t and α a constant.
management unit).
The studies have shown that for different conditions, such as switch/buffer size and traffic phase, an α value between 2-1 and 2 is appropriate [1][3].
A. SBS Model An NxN SBS consists of a buffer management unit that is responsible from storing buffer state, allocating space for newly arrived packets and
function was first studied in [6] on the basis of single
updated at every space request from one of the queue
server queuing model with the input traffic
controllers. Queue controllers accept newly arrived
characterised by the Poisson arrivals. This scheme
packets and deliver packets at the head of the queue.
states that packets are admitted or blocked by using a
Based on the threshold value, packet is granted a
notion of fullness (Fig. 1).
space or blocked. Each queue controller serves one
Blocking Probability
B. Sigmoid Function Threshold The use of sigmoid shaped membership
calculating the threshold value. Threshold value is
packet per frame-time 1 (i.e. deterministic service
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
time). A one-packet space is returned to the buffer management unit whenever a packet leaves the switch. B. Traffic Model Inputs of SBS are connected to N independent asynchronous traffic generators each of which generates fixed length packets. At most one packet is
Buffer Occupancy (%)
Fig. 1 – Sigmoid shaped packet-blocking scheme
generated during a frame-time. Each traffic generator is a realisation of an Interrupted Poisson Process (IPP)
This scheme can be easily utilised in SBSs.
[7]. The time spent in ON and OFF states is
That is, probability of blocking a packet arriving at
exponentially distributed with mean durations of TON
the queue of port i at time t is given by:
and TOFF respectively. Arrivals occur only at ON states with rate λ. Thus, the traffic load can be
µ bi (t ) =
1 1 + e c. a
q i (t ) and c = M .β
(2)
Where q (t) is the length of queue i at time t, M is the
formally presented by:
p=
i
size of shared buffer and β is the maximum allocation (0 < β ≤ 1). Parameter a defines the steepness of the
maximum allocation (M. β).
(3)
IV. Results and Discussions
fixed rather than fuzzy. Regardless of the overall individual buffer usage within the permissible
TON + TOFF
Traffic distributions considered in our simulations are symmetric and asymmetric scenarios.
curve. For very large a, the accept/reject policy is buffer occupancy, SFT takes into account the
λ.TON
In our simulations we considered a 32x32 switch with 640-packet space shared among 32 1
Frame-time is the duration of a packet.
output ports. Input load is 0.8 and the mean burst 4.60E-01
SFT-3
asymmetric distributions. Also, in all of the
4.10E-01
SFT-4
simulations DT α value is set to 1.0.
3.60E-01
SFT-5
3.10E-01
DT
In Figure 2, we considered both symmetric and asymmetric loads. When the load is symmetric,
PLR
duration is 100 frame-times with symmetric and
2.60E-01
where all of the output ports receive the same amount
2.10E-01
of traffic load (0.8), optimal β value is observed as
1.60E-01
1.0 and SFT achieves the same packet loss rate (PLR)
1.10E-01
as DT. However, in case of asymmetric loads where
6.00E-02
hotspot ports receive 0.95 and 1.05 loads, β value has to be within the range of 0.20 and 0.25 in order to achieve the lowest possible PLR. Therefore, one could state that a full share is needed for SFT when
0
1.95E-01
ports, optimal β value is between 0.20 and 0.25. Unlike DT, SFT employs a separate admission (threshold) for every queue and its performance is bounded with the β value. For this reason, share parameter (β) has to be at an optimal level in order to limit the queue lengths of heavily loaded output ports or a full share has to be employed in case when there is a uniformly distributed traffic.
DT(1.0)
1.55E-01
The result of a similar test is depicted in Figure
is observed. Regardless of the number of hotspot
SFT(0.25)
1.75E-01
β defines the level of buffer space sharing.
1.35E-01 PLR
(0.95) and the effect of different number of hotspots
1
Fig. 3 – Packet loss rate against β value of SFT for different number of hotspot ports
the traffic is uniformly distributed and the parameter
3. In this case hotspot load is set to a fixed value
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 beta
1.15E-01 9.50E-02 7.50E-02 5.50E-02 3.50E-02 0
1
2
3
4
5
6
7
8
No. of heavily loaded ports
Fig. 4 – Packet loss rate against the number of heavily loaded hotspot ports In Figure 4, we compared the performances of both schemes using a fixed hotspot load (0.95) while varying the number of heavily loaded ports. Also, β
5.00E-01 4.50E-01 4.00E-01
PLR
3.50E-01
SFT-0.8
is selected as 0.25 for SFT. SFT scheme achieves a
SFT-0.95
reasonably close performance to DT. As the number
SFT-1.05
of hotspots increases, PLR performances of both of
DT
3.00E-01
the schemes are expected to be approximately the
2.50E-01
same due to saturation of the buffer.
2.00E-01
In Figures 5 and 6, we considered the buffer
1.50E-01
occupancies of hotspot ports and unused buffer space
1.00E-01
under asymmetric input traffic for a given duration of
5.00E-02
simulation time. As can be seen in Figure 5, the
0.00E+00 0
0.1 0.2
0.3 0.4 0.5 0.6 0.7 beta
0.8 0.9
Fig. 2 – Packet loss rate against β value of SFT for various hotspot loads
1
available buffer space in SFT scheme is affected by the ON and OFF periods of the input traffic. However, in DT scheme, the available buffer space is determined by the active ports (Figure 6). Besides, buffer occupancy of active ports in SFT is rather steady when compared to DT. The reason for this is
that the sigmoid shaped membership function is
out to compare the performance of SFT with the
applied to all of the queues individually. As a result,
well-known DT.
the lengths of all of the queues, regardless of whether
The
results
presented
show
that
under
they are active or not, are controlled in the same way.
symmetric ON-OFF input traffic the optimal β value
On the other hand, DT scheme controls only those
for SFT is 1.0; whereas for asymmetric ON-OFF
queues that are highly active. Hence, lightly loaded
traffic β value is between 0.20 and 0.25. SFT
queues are allowed to grow and the maximum busy
achieves a reasonably good packet loss rate when
periods of each queue is increased [4].
compared to DT. It uses a multiple packet admission
The buffer space that SFT scheme spares for
scheme rather than a single threshold. The main
lightly loaded ports is underutilised due to the
drawback is that even the lightly and moderately
sigmoid membership control of the lightly loaded
loaded queues undergo this control scheme and they
queues. However, DT scheme spares enough space
are not allowed to grow freely. As a consequence,
for lightly and moderately loaded queues to grow
buffer space spared by very active queues is
freely. Nevertheless, this scheme still performs worse
underutilised.
than the well-known DoD, because some space is still wasted.
Although, SFT performs slightly worse than DT, its performance is promising and it can be tuned by applying the admission scheme only to very active
190 Hotspot ports Unused space
170
queues.
Queue length
150
VI. References
130
[1] M. Arpaci and J. A. Copeland, “Buffer Management for Shared-Memory ATM Switches,” IEEE Communications Surveys, First Quarter 2000.
110 90 70 50 30 0
2000
4000 6000 Simulation time (t)
8000
10000
Fig. 5 – Transient buffer occupancy of SFT in time (3 hotspot ports with 0.95 load each) 130 Hotspot ports
120
Unused space
110
Queue length
100
[2] S. X. Wei, E. J. Coyle, and M. T. Hsiao, “An optimal buffer management policy for high performance packet switching,” IEEE GLOBECOM'91, Vol. 2, Dec. 1991, pp.924-928. [3] A. K. Choudhury , and E. L. Hahne, “Dynamic queue length thresholds for shared-memory packet switches,” IEEE/ACM Transactions on Networking (TON), Vol.6, No.2, Apr 1998, pp.130-140. [4] S. Sharma, and Y. Viniotis, “Optimal buffer management policies for shared-buffer ATM switches,” IEEE/ACM Transactions on Networking. Vol.7, No.4, Aug. 1999, pp.575-587.
90 80 70 60 50 40 30 0
2000
4000
6000
8000
10000
[5] G. Ascia, V. Catania, and D. Panno, “An Efficient Buffer Management Policy Based On An Integrated Fuzzy-GA Approach”, IEEE/ACM INFOCOM, June 2002.
Simluation time (t)
Fig. 6 – Transient buffer occupancy of DT in time (3 hotspot ports with 0.95 load each)
V. Summary In this paper, we adapted the sigmoid membership function in order to be used in shared buffer switches. A simulation study has been carried
[6] A. Bonde, and S. Ghosh, “A Comparative Study of Fuzzy versus ‘Fixed’ Threshold for Robust Queue Management in Cell-Switching Networks,” IEEE/ACM Transactions on Networking, Vol.2, No.4, August 1994, pp.337-344. [7] A. Adas, “Traffic Models in Broadband Networks,” IEEE Communications Magazine, July 1997, pp. 82-89.
