Dynamic bandwidth allocation scheme in lr pon with performance modelling and analysis

International Journal of Computer Networks & Communications (IJCNC) Vol.6, No.2, March 2014
DOI : 10.5121/ijcnc.2014.6201 01
DYNAMIC BANDWIDTH ALLOCATION SCHEME IN
LR-PON WITH PERFORMANCE MODELLING AND
ANALYSIS
Tony Tsang1
1
Department of Computer Science and Computer Engineering,
La Trobe University, Melbourne, Australia
ABSTRACT
We consider models of telecommunication systems that incorporate probability, dense real-time and data.
We present a new formal abstraction method for computing minimum and maximum reachability
probabilities for such models. Our approach uses strictly local formal abstract steps to reduce both the size
of abstract specifications generated and the complexity of operations needed, in comparison to previous
approaches of this kind. A selection of large case studies are implemented the techniques and evaluate,
which include some infinite-state probabilistic real time models, demonstrating improvements over existing
tools in several cases. The capacity of metro and access networks are extended the reach and split ratio of
the conventional Long - Reach Passive Optical Networks (LR-PONs). The efficient solutions of LR-PONs
are appeared in feeder distances around 100km and high split ratios up to 1000-way . Among many
existing approaches, one of the most effective options to improve network performance in LR-PONs are the
multi-thread based dynamic bandwidth allocation (DBA) scheme where several bandwidth allocation
processes are performed in parallel is considered. Without proper intercommunication between the
overlapped threads, multi-thread DBA may lose efficiency and even perform worse than the conventional
single thread algorithm. Real Time Probabilistic Systems are used to evaluate a typical PON systems
performance. This approach is more convenient, flexible, and lower cost than the former simulation method,
which do not need develop special hardware and software tools. Moreover, how changes in performance
depend on changes in the particular modes can be easily analysis by supplying ranges for parameter values.
The proposed algorithm with traditional DBA is compared, and shows its advantage on average packet
delay. The key parameters of the algorithm are analysed and optimized, such as initiating and tuning
multiple threads, inter -thread scheduling, and fairness among users. The algorithms advantage in
numerical results are decreased the average packet delay and improve network throughput under varying
offered loads.
KEYWORDS
Long- reach Passive Optical Networks; Dynamic Bandwidth Allocation; Real Time Probabilistic Systems;
Performance Analysis;
1. INTRODUCTION
Formal Modelling is a highly successful approach to the performance analysis of complex
infinite-state systems. The basic idea is to construct a sequence of increasingly precise
abstractions of the system to be verified, with each abstraction typically over-approximating its
behaviour. Through a process of refinement which terminates once the abstraction is precise
enough to verify the desired property of the system under analysis, construct the successive
abstractions. Formal techniques have also been used to verify probabilistic systems, including
those with real-time characteristics and continuous variables. Frequently, though, the high

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complexity of both the abstractions involved and the operations needed to construct and refine,
which hinder the practical implementations of these techniques.
In this article, the performance analysis of systems is targeted, whose behaviour incorporates both
probabilistic and real-time aspects, and which include the manipulation of (potentially infinite)
data variables. Real Time Probabilistic Systems (RTPS) are modelled, whose semantics are
defined as infinite-state Markov decision processes (MDPs) [1]. A formal abstraction procedure is
introduced for computing minimum and maximum reachability probabilities in RTPS. This
provides outer bounds on reachability probabilities (i.e., a lower bound on the minimum
probability or an upper bound on the maximum). In addition, the inner bounds and based on a
stepwise concretization of adversaries of this abstract MDP are computed, yielding upper and
lower bounds on minimum and maximum probabilities, respectively. Untimed models used
concretization. The key difference in our work is kept the abstraction small by using local
refinement and simplification operations, so as reducing the need for expensive operations such as
Craig interpolation.
The formal abstraction loop repeated to attempt constructing a concrete adversary of the RTPS.
Based on the exploration of the part of the state space, which is the current abstract adversary can
be concretized. In each exploration step, an inconsistency is encountered, in which case we derive
a formal operation and restart. Otherwise, the constructed adversary is numerically solved, giving
inner bounds on the desired probability values. The difference between upper and lower bounds is
smaller than a specified threshold is terminated the formal abstraction loop. The formal
abstraction approach are implemented; deploy it on various large case studies, and compare to the
probabilistic verification tools PRISM [2], are illustrated to improve performance in many cases.
Real Time Probabilistic Systems enable to verify and containing both real-time behaviour and
infinite data variables, which this tool can be handle.
The high bandwidth of high-capacity communication systems (e.g., optical fibre) are bring closer
to the remote end users with affordable costs, the long-reach passive optical network (PON) was
introduced and studied over the past few years. The LR-PON are developed coinciding with the
momentum in the integration of metro and access networks, as well as the integration of wire line
and wireless networks. The hierarchical architecture of the telecommunication network are
simplified and can significantly reduce both capital expenditure (CapEx) and operational
expenditure (OpEx) by lowering the total number of active sites, such as points of presence
(PoPs) and local exchanges (LXs). Three parts are consisted in a typical PON: the optical line
terminal (OLT) at the telecom central office (CO), optical network units (ONUs) located at end
users’ premises and remote nodes (RNs) in between, as shown in Figure 1. To provide high
bandwidth to a large number of users in an LR-BAN, hybrid architecture should be deployed,
exploiting both time-division multiplexing (TDM), where a single wavelength channel is shared
among multiple users and wavelength-division multiplexing (WDM), which supports multiple
wavelengths to increase capacity.
However, the traditional PONs are relatively small span and inflexible topology of restrict a
Broadband Access Networks from reaching remote users. Extend the coverage of PONs in both
directions are do the research. In the network direction, the long-reach PON (LR-PON) [3] it is no
longer a passive structure has been proposed to extend the coverage from 20 to 100 km by
exploiting advanced technologies such as reflective semiconductor optical amplifiers (R-SOAs)
and burst-mode receivers. Instead of copying the traditional ``tree-and-branch’’ topology in
PONs, researchers are also investigating a ``ring-and-spur'' topology for LR-PONs [3], as shown
in Figure 2, where a PON segment consists of the OLT and a set of ONUs operating on a
wavelength set; each PON segment exhibits a logical tree topology; several such PON segments
coexist; and the OLT and ONUs are connected through a fibre ring, and RNs are deployed on the

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ring. Although, additional RNs are introduced increasing the overall complexity of the network,
an advantage of this design is that the metro synchronous optical network / digital hierarchy
(SONET/SDH) ring networks with fibre can be reused already deployed by substituting the RN
equipment and thus achieve great savings in CapEx. This ring-and-spur topology can not only
cover a larger area than the traditional tree topology, but also provide the broadband access
networks two-dimensional coverage for failure protection, which is very important today as strict
quality of service (QoS) may be specified in a user’s service level agreement (SLA). The
introduction of the paper has been explained the nature of the problem, previous work, purpose,
and the contribution of the paper. The contents of each section may be provided to understand
easily about the paper.
Figure 1. PON Architecture
Figure 2. Ring and Spur LR-PON
The PON standards have adopted Time-division multiple access (TDMA), Ethernet PON
(EPON) and Gigabit PON (GPON), to share the optical capacity among subscribers by assigning

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different timeslots for each user. Centralized dynamic bandwidth allocation (DBA), in which the
OLT at the CO arbitrates time-division access to the shared upstream channel. The round-trip
time (RTT) are depended on performance of centralized allocation, since it imposes a delay on the
OLT-ONUs bandwidth allocation control loop. This delay is not as significant in traditional PONs
as it is in LR-PONs, where the reach extension may cause the RTT to grow from todays 200 µs
(20 km reach) to 1 ms (100 km reach). The performance of centralized DBA is ultimately
degraded with this is increased.
multi-thread polling and inter-thread scheduling are reviewed and analysed, which is a recently
proposed bandwidth allocation algorithm for LR-PONs, and traditional interleaved polling is
compared. Unexpectedly, the overall packet delay performance of the latter is found better than
the recently proposed multi-thread polling scheme. Our investigation highlights how multi-thread
polling looks compelling for LR-PONs compared to single thread polling only when the latter is
assumed to be scheduled offline. The offline scheduling is used a single thread leaves a long idle
period that the multi-thread scheme utilizes by creating additional threads. However, while
traditional inter-thread polling is a single-thread scheme, online scheduling is exploited with
extremely small idle times. The demonstration of key results are that inter-thread polling with
online scheduling better reduces the overall packet delay in addition to better utilizing the
upstream channel. In the paper, some inaccuracies are pointed out in the multi-thread algorithm,
and suggest some modifications.
The rest of the paper is organized as follows. In Section II we give a brief introduction to Real
Time Probabilistic Systems. Next, we review PRISM Probabilistic Model Checker in Section III,
explaining how its performance analysis is highly affected by extending the network span. In
Section IV, we review multi-thread polling and discuss the different aspects of its algorithm,
highlighting its major differences from enhanced inter-thread scheduling. Section V presents
illustrative numerical results, and Section VI concludes the study.
2. REAL TIME PROBABILISTIC SYSTEMS
The definition of real time probabilistic system is reviewed in this section, both nondeterministic
and stochastic behaviour are exhibited in the modelling framework for real-time systems. The
extending classical timed automata with discrete probability distributions over edges derive the
formalism. First, standard notation is introduced for clocks and zones of timed automata, and then
we proceed to the definition of probabilistic timed automata [4, 5, 6]. At the end of this section,
Probabilistic Timed Computation Tree Logic (PTCTL) is introduced as a probabilistic timed
temporal logic for the specification of properties of probabilistic timed automata.
2.1. Clocks and Zones
Let X is a finite set of variables called clocks which take values from the time domain 0≥ℜ
(non-negative reals). A function 0:v ≥→ ℜX is referred to as a clock valuation. The set of all
clock valuations is denoted by 0≥ℜX
. For any 0v ≥∈ℜX
and 0t ≥∈ℜ , we use v + t to denote the
clock valuation defined as (v + t)(x) = v(x) + t for all x∈X . We use v[X := 0] to denote the
clock valuation obtained from v by resetting all of the clocks in X ⊆ X to 0, and leaving the
values of all other clocks unchanged; formally, v[X := 0](x) = 0n if x ∈ X and v[X := 0](x) = v(x)
otherwise.
The set of zones ofX , written Zones (X ), is defined inductively by the syntax:
ς :: = x ≤ d | c ≤ x | x + c ≤ y + d | ¬ς | ς ∨ ς

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Where x, y ∈ X and c, d ∈ N. As usual, ς1 ∧ ς2 = ¬(¬ς1 ∨ ¬ς2) and strict constraints can be
written using negation, for example x > 2 = ¬(x ≤ 2) .
The clock valuation v satisfies the zone ς, written v ς> , if and only if ς resolves to true after
substituting each clock v ς> with the corresponding clock value v(x) from v . Intuitively, the
semantics of a zone is the set of clock valuations (subset of 0≥ℜX
) which satisfy the zone. Note
that more than one zone may represent the same set of clock valuations (for example, (x ≤ 2) ∧ (y
≤ 1) ∧ (x ≤ y + 2) and (x ≤ 2) ∧ (y ≤ 1) ∧ (x ≤ y + 3)). We hence forth consider only canonical
zones, which are zones for which the constraints are as tight as possible. For any valid zone
Zonesς ∈ X , there exists a 3
(O X∣ ∣) algorithm to compute the (unique) canonical zone of ς .
This enables us to use the above syntax for zones interchangeably with semantic, set-theoretic
operations.
We require the following classical operations on zones [4, 6]. For zones ς, ς′ ∈ Zones(X) and
subset a of clocks X ⊆ X , let:
↙ς′ ς = {v | ∃ t ≥ 0.(v + t ς ∧ ∀ t′ ≤ t.(v + t′ ς ∨ ς′))}
[X := 0]ς = {v | v[X := 0] ς}
ς[X := 0] = {v[X := 0] | v ς} .
The zone↙ς′ ς contains the clock valuations that can, by letting time pass, reach a clock valuation
in ς and remain in ς′ until ς is reached. The zone [X := 0]ς contains the clock valuations which
result in a clock valuation in ς when the clocks in X are reset to 0. The zone ς[X := 0] contains the
clock valuations which are obtained from clock valuations in ς by resetting the clocks in X to 0.
2.2. Syntax and Semantics of Real Time Probabilistic Systems
We now present the formal syntax of Real Time Probabilistic Systems.
Timed Action
A tuple < α, λ, T > of timed action consisting of the type of the action α , the rate of the action λ
and temporal constraint of the action T . The kind of action is denoted the type, such as
transmission of data packets, while the rate indicates the speed at which the action occurs from
the view of an external observer. The random variables rate use to denoted specifying the duration
of the actions. The different types of probability distribution function define the actions such as
Exponential, Poisson, Constant, Geometric and Uniform distribution. Moreover, each transition is
also bounded by a temporal constraint. In this section, Real Time Probabilistic Systems briefly
introduce some basic notations and operation semantics. The syntax of Real Time Probabilistic
Systems is defined as follows:
P ::= stop | < α, λ,T > . P | P + Q | P ⊕r,T Q | P ▹ ◃L,T Q | P ▽△ P,T Q | P/L | A
The conventional stochastic process algebra operators and the additional operations are described
in the following:

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• stop is an inactive process.
• < α, λ,T > . P , which stands for a prefix operator, where the type of the action is a probability
distribution function (pdf) type α , with the activity rate denoted by λ , and the temporal constraint
of component is T .
It subsequently behaves as P. Sequences of actions can be combined to build up a time constraint
for an action. The time constraint T is defined as above.
• P + Q is choice combinatory capturing the possibility of competition or selection between
different possible Activities. It represents a system which may behave either as P or as Q. All the
current actions P and Q are enabled. The first action to complete distinguishes one of the
processes. The other process of the choice is discarded. The system will then behave as the
derivative resulting from the evolution of the chosen process.
• P ⊕r,T Q denotes the probabilistic choice with the conventional generative interpretation, thus
with probability r the process behaves like P and with probability 1 − r it behaves like Q bounded
with the time constraint T .
• P ▹ ◃L,T Q is a cooperation, in which the two actions P and Q are parallel, synchronizing on all
activities whose type is in the cooperation set L of action types. The lifetime of two actions is the
time constraint T . These two actions are disabled when the time constraint expires. Any action
whose type is not in L will proceed independently. As a syntactic convenience the parallel
combinator is defined by ▹ ◃ϕ,T , where the cooperation set L is empty and the lifetime of two
actions is T .
• P ▽△ P,T Qis a unary operator which returns the set of actions that meet the temporal predicate
condition specified by T . P consists of several predicates combined with the boolean connectives:
‘And’ ,‘Or’, Exclusive-Or (EXOR)’ and ‘Not’. ▽△ And,T means both actions can occur during the
interval T . ▽△ Or,T means that one or both actions can occur during the interval T . ▽△ EXOR,T
means that one of these actions occurs; it immediately determines whether P or Q can
subsequently occur during the triggered interval T . ▽△ Not,T means that both actions do not
occur during the interval T .
• P/L is a hiding operation, where the set L of visible action types identifies those activities which
are to be considered internal or private to the component. These activities are not visible to an
external observer, nor are they accessible to other components for cooperation.
• A := P is a countable set of constants.
2.3. Probabilistic Timed Computation Tree Logic
We now describe Probabilistic Timed Computation Tree Logic (PTCTL) which can be used to
specify properties of probabilistic timed automata. This logic is a combination of two extensions
of the temporal logic CTL [7], the timed logic TCTL [8] and the probabilistic logic PCTL [9].
The logic TCTL employs a set of formula clocks, Z, disjoint from the clocks X of the
probabilistic timed automaton under study. Formula clocks are assigned values by formula clock
valuations ϕ ∈ RZ ≥0. The logic TCTL can express timing constraints and includes the reset

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quantifier z. ϕ, used to reset the formula clock z so that the formula ϕ is evaluated from a state at
which z = 0. PTCTL is obtained by enhancing TCTL with the probabilistic quantifier P∼λ[.] from
PCTL and removing the path quantifiers ∃ and ∀ .
The syntax of PTCTL is defined as follows:
ϕ ::= a | ζ | ¬ϕ | ϕ ∨ ϕ | z.ϕ | P∼λ[ϕUϕ] | P∼λ[ϕVϕ]
where a ∈ AP, ζ ∈ Zones(X ∪ Z), z ∈ Z, ∼∈ {≤, <, >, ≥} and λ ∈ [0, 1] . We use the abbreviations
⋄ϕ and 2ϕ for true Uϕ and false Vϕ respectively. In PTCTL we can express properties such as:
• with probability strictly greater than 0.96, the system delivers packet 1 within 5 time units and
does not try to send packet 2 in the meantime, which is represented by
z.P>0.96[packet2unsentU(packet1delivered ∧ (z < 5))] ;
• with probability at least 0.93, the system clock x does not exceed 3 before 8 time units elapse,
which is represented as z.P>0.93[(x ≤ 3)U(z = 8)] ;
• the system remains up after the first 60 time units have elapsed with probability greater than
0.97, represented as z.P>0.97[2(system up ∨ (z ≤ 60))] .
Next, we define the semantics of PTCTL. We write v, ϕ to denote the composite clock valuation
in obtained from 0v ≥∈ℜX
and 0≥∈ℜZ
ò . Given a state and formula clock valuation pair (l, v), ϕ ,
zone ζ and duration t , by abuse of notation we let ( , ),l v ζ>ò denote ,v ζ>ò v, and (l, v) + t
denote (l, v + t) .
3. PRISM PROBABILISTIC MODEL CHECKER
Model checking for several types of probabilistic models are provided in Prism [2]:
discrete and continuous time Markov chains and Markov decision processes, as well as a
modelling language in which to express them. The tool has been widely taken up and
used for quantitative verification in a broad spectrum of application domains, from
wireless communication protocols to quantum cryptography to systems biology.
3.1. Overview of Functionality
We begin with a brief overview of the current functionality of the prism tool. Items are
the new or improved features in version 4.0, which are described in more detail in the
remainder of the paper.
• many types of probabilistic models are modelled and constructed, now including
probabilistic timed automata; all can be augmented with costs or rewards, in the case of
PTAs yielding the model of priced probabilistic timed automata;
•a wide range of quantitative properties are the model checking, expressed in a language
that subsumes the temporal logics PCTL, CSL, LTL and PCTL*, as well as extensions
for quantitative specifications and costs/rewards;

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•both symbolic (BDD-based) and explicit- state multiple are model checking engines; and
a variety of probabilistic verification techniques, such as symmetry reduction and
quantitative abstraction refinement;
•with support for statistical model checking methods are the discrete-event simulator,
including confidence-level approximation and acceptance sampling;
• Model import options, e.g. From SBML (systems biology mark-up language);
• Optimal adversary/strategy generation for nondeterministic models;
• With model editor is a GUI, simulator and graphing, or command-line tool;
• Probabilistic models and associated properties in benchmark suite.
4. MULTI-THREAD SCHEDULING SCHEME OF DYNAMIC
BANDWIDTH ALLOCATION
In this section, we briefly describe two different inter-thread scheduling algorithms
presented in [10, 11, 12] in Figure 3. The one proposed in [12] is referred to as newly
arrived plus (NA+), which aims to overcome the over granting problem in multithread
schemes. We name the reviewed algorithm (i.e., in [10] ) as subsequent requests plus
(SR+), since it is able to reduce grant delay by utilizing the information regarding the
requests received in the overlapped subsequent DBA processes. Furthermore, we
integrate the key advantages of these two existing approaches and propose an enhanced
inter-thread scheduling (EIS) algorithm in order to further improve the DBA performance.
All the notations used for the description of the algorithms are listed as follows:
M : Total number of active ONUs
N : Total number of threads
Bi,n : Actual bandwidth demand for ONUi in DBA process n
min
iB : Predefined guaranteed minimum bandwidth for ONUi
Ri,n : Bandwidth reported from ONUi in DBA process n (i.e., the buffer status of ONUi
at time ti,n )
R’i,n : OLT based on Ri,n are recalculated bandwidth request, and the associated inter-
thread scheduling schemes
Gi,n : Resulting grant to ONUi responding to Ri,n
gi,n : Actual bandwidth for data transmission between ti,n−1 and ti,n at ONUi
Ai,n : New traffic that arrived to ONUi between ti,n−1 and ti,n
Ui,n : Unused time slots occurrence during the nth DBA process at ONUi
Ci,n : A term to compensate backlogged traffic
The overall system specification becomes ONU and OLT:
OLT := ONU0 < λ1 > ONU1 < λ2 > ONU2 < λ3 > • • • •

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Figure 3. Mult-Thread DBA processes between an OLT and an ONU.
4.1. Newly Arrived Plus
Over-granting can be a serious performance issue in a typical LR-PON scenario when a
multi-thread DBA scheme is used. To overcome this problem, Newly Arrived Plus (NA+)
has been proposed in the literature [12]. The main idea of NA+ is that each thread is
mainly responsible for the bandwidth allocation for the traffic that has arrived since the
initiation of the last DBA process. In this way load is evenly distributed among the
different threads. NA+ can compensate for the backlogged traffic at a specific ONUi in
DBA process n using the information gathered from some previously completed DBA
process. A compensation mechanism for backlogged traffic is important because a DBA
allocation process may not be able to cater for all the requested bandwidth in a given
DBA process. Furthermore, EPON does not support frame fragmentation, and unused
time slots (UTS) may occur. NA+, presented in [12], also includes a compensation
mechanism for the UTS in EPONs. The effectiveness of NA+ can be clearly observed
from [12], where an over-reporting problem is eliminated by allocating bandwidth only
once. For instance, the first arrived packet (i.e., the black packet) is reported in both Ri,1
and Ri,2 , but the corresponding bandwidth granting is only performed once (i.e., in Gi,1 )
because R’i,2 excludes the bandwidth of the black packet, which has already been
granted in Gi,1. This allows improving network throughput as well as delay and jitter.
The operation in Newly Arrive Plus multi-thread DBA Scheme for ONUi specified as
follows:
ONUi := < sent, λ1 > . Report(R)i,1 ▹◃L1 < get, λ1 > . OLT ;
ONUi := < poll, delayi > . Report(R)i,2 ▹◃L2 < get, λ2 > . OLT ;

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ONUi := < grantNA+, delayNA+i > . Datai ▹◃L3 < get, λ3 > . OLT ;
ONUi := < sent, delayi > . Report(R)i,3 ▹◃L4 < get, λ4 > . OLT ;
ONUi := < queue, delayi > . Datai ▹◃L5 < get, λ5 > . OLT ;
The operation in DBA Scheme for OLT specified as follows:
OLT := < sent, delay1 > . Result(G)i,1 ▹◃L1 < get, λ1 > . ONU1 ;
4.2. Subsequent Requests Plus
In Subsequent Requests Plus (SR+) [10, 11], an inter-threading mechanism is introduced
that allows bandwidth allocation even for the packets that arrived at an ONU queue after
issuing the report for the current DBA process. Therefore, this mechanism to perform
bandwidth allocation for subsequent requests can reduce packet delay noticeably in many
cases. [10] gives an example of SR+ employed in a two-thread DBA. Before calculating
the bandwidth allocation for the Ri,1, Ri,2 is also available. So some packets queuing at
the ONUi after the transmission of Ri,1 do not have to wait for the receipt of Gi,2 to be
transmitted because they have been considered in R’ i,1 before Gi,2 is issued and hence
could be transmitted as soon as Gi,1 is received. This clearly reduces the dgrant for the
light grey packet shown in Fig. 3b. It should be noted that two packets are reported in
Ri,2, but there is still a risk that not both of them can be transmitted after receiving Gi,1 ,
because the bandwidth request cannot always be satisfied. Furthermore, the over-granting
problem cannot be avoided in SR+. For instance, the black packet is considered twice in
R’ i,1.
The operation in Subsequent Requests Plus multi-thread DBA Scheme for ONUi
specified as follows:
ONUi := < sent, λ1 > . Reporti,1 ▹◃L1 < get, λ1 > .OLT ;
ONUi := < poll, delayi > . Reporti,2 ▹◃L2 < get, λ2 > .OLT ;
ONUi := < grantSR+, delaySR+i > . Datai ▹◃L3 < get, λ3 > .OLT ;
ONUi := < sent, delayi > . Reporti,3 ▹◃L4 < get, λ4 > .OLT ;
ONUi := < queue, delayi > . Datai ▹◃L5 < get, λ5 > .OLT ;
4.3. Enhanced Inter-Thread Scheduling
Our proposed enhanced inter-thread scheduling (EIS) is a hybrid scheme capturing key
ideas from both NA+ and SR+ to improve DBA performance in a multi-thread
environment. For bandwidth granting, we consider a newly arrived packet as in NA+ to
effectively eliminate the over-reporting problem, while bandwidth requested in the
subsequent DBA processes is also taken into account as in SR+ if it arrives before the
calculation of the bandwidth granted in the current DBA process. Pseudo code for the EIS

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scheme is outlined in [11]. Benefits of employing EIS can be seen clearly from [11]
where d grant of the packet with the white colour can be significantly reduced compared
to NA+ and SR+. This is because R′i,1 can correctly reflect the current bandwidth request.
The traffic reported in Ri,2 can be taken into account when issuing Gi,1 . Furthermore, by
eliminating the over-reporting for the black packet (which has been reported twice), both
packets that arrived after Ri,1 at ONUi can be transmitted after receiving Gi,1 .
Performance in a PON system is sensitive to DBA computation time, particularly in a
multi-thread environment where several threads in parallel increase the complexity. In
this regard, our proposed EIS scheme does not require any additional inter-thread
communication mechanism compared to NA+ and SR+. In other words, there is no
explicit control information that needs to be exchanged between the threads (except for
the usual report messages), so the DBA complexity grows linearly relative to a single-
thread implementation. However, due to DBA control messages in each thread, there is
still a linear increase in overhead with respect to the employed number of threads.
Consequently, it may lead to degraded performance by increasing the number of threads
beyond a certain level, as the added control messages introduced by the extra threads
could decrease the bandwidth utilization and affect the other performance measures such
as delay and jitter. As shown in the next section, in most of the evaluated cases applying
two or three threads is optimal to gain the maximum benefit depending on the specific
reach scenario as well as the employed multi-thread algorithm. The operation in
Enhanced Inter-Thread Scheduling for ONU1 specified as follows:
ONUi := < sent, λ1 > . Reporti,1 ▹◃L1 < get, λ1 > . OLT ;
ONUi := < poll, delayi > . Reporti,2 ▹◃L2 < get, λ2 > . OLT ;
ONUi := < sent, delayi > . Reporti,3 ▹◃L3 < get, λ3 > . OLT ;
ONUi := < grantEIS, delayEISi > . Datai ▹◃L4 < get, λ4 > . OLT ;
ONUi := < waitEIS, delayEISi > . Datai ▹◃L3 < get, λ5 > . OLT ;
ONUi := < queue, delayi > . Datai ▹◃L6 < get, λ6 > . OLT ;
5. PERFORMANCE EVALUATION
Several well-known benchmarks for the cyclic redundancy check problem are evaluated
on the procedure. First, parametrisable case study is used to present evidence that the
algorithm gives correct answers and then we present systematic comparisons with PRISM.
The PRISM simulation framework is extended for sampling purposes. Because we use
the same input language as PRISM, many off-the-shelf models and case studies can be
used with our approach.
5.1. Performance Result
We simulate a LR-PON with M-ONUs. Single or multiple wavelengths are used to carry
the upstream traffic, depending on the aggregated user requests. The problem are made
clear and focused on packet delay, we assume that the M-ONUs share the same upstream
channel (one upstream wavelength). If more users join the network, a new upstream

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channel can be assigned to them and the same polling scheme is implemented on the new
channel independently.
From the access side, an ONU are arrived packets from a user connected to the ONU. The
ONU buffered the packets until the ONU is allowed to transmit them to the OLT. In our
model, we consider RD to be the data rate of the access link from a user to an ONU, and
RU to be the date rate of the upstream channel from ONU to OLT. Note that, if RU < M
× RD, there are exist the bandwidth utilization problem, because the system capacity is
greater than the aggregated load from all ONUs. (The steady-state case is, but during
temporary overload situations due to burst traffic, the load may be higher than capacity.)
So, we choose M = 16 and RU and RD to be 1 Gbps and 100 Mbps, respectively.
Packets are generated in the form of Ethernet frames (64 to 1518 bytes) and they arrive at
each ONU from the end user. The property of Internet traffic is reflected, the generated
user traffic is self-similar by aggregating multiple sub-streams, each consisting of
alternating Pareto-distributed on/off periods, with a Hurst Parameter of 0.8. The buffer
size at each ONU is limited to 10 Mbytes.
The performance of our multi-thread polling algorithm are studied, the LR-PON are
simulated in two different scenarios, where ONUs is 20 km and 100 km from the OLT,
respectively. 0.5s sets in the initial interval of threads for the 100-km scenario and 0.3 s
for 20-km scenario, which represent maximum cycle duration (RTT); the tuning threshold
θ tune is set to be 5 in the simulation. The benefit of multi-thread is highlighted polling
on the average packet delay, the constraints are dropped on single-thread polling by
allowing it to ignore the fairness issue, and thereby the idle time is not counted.
From the results shown in Figure 4, high load (0.8) scenarios can observe ; delay
performance improvement is tangible in EIS compared to NA+ and SR+. The
performance can be noted in hit due to multi-threading through the increased overhead
associated with report and grant messages. For this reason, all the multi-thread schemes
perform worse when tested in the three thread case than in the two thread one. Increasing
the number of threads by more than two affects the DBA performance are introduced
extra control overhead. This performance degradation is more severe in SR+ than the
other two schemes where the over-granting problem is well treated. Besides, in NA+ and
EIS, the performance three thread cases become less obvious when the reach increases.
Because of the longer reach, the increased overhead incurred by a three thread
implementation is compensated more by the gain of introduction of one more thread than
in the two thread case. In particular for the reach of 100 km and beyond for both EIS and
NA+ three thread implementations provides better performance. High load (0.8) is true
for the statement as similar behaviour for the different schemes can be seen in the high
load situation (0.8) as well, although the absolute values for delay are larger because
higher load leads to much longer average round-trip time (RTT) per thread. EIS still
performs best, while NA+ performs the worst in the high load scenario. According to the
results shown in Figure 4, three is generally the optimal number of threads are found for
the schemes presented here in order to obtain the best delay performance except for reach
of 100 km and beyond, where a three thread implementation performs better, as explained
above, for both EIS and NA+. Furthermore, this value is also dependent on system

13
characteristics (number of ONUs, line rate, buffer size, etc.) and traffic profile (load,
burstiness, etc.).
The different schemes of jitter performance are shown in Figure 5 for high (0.8) load,
respectively. EIS can saw that has the lowest jitter for three thread cases. NA+ shows
decent jitter performance but at the expense of worse delay performance, as shown earlier.
SR+ with jitter performance is very dependent on the number of threads employed. The
best performance is shown the three thread implementation at high load but it gets
significantly worse for the three thread implementation where the over-granting problem
is more intense. Apart from this observation, jitter performance for different schemes is
close at high loads.
The last set of results shown in Figure 6 is for the throughput. EIS has the highest
throughput under both low and high load conditions. As noted earlier for reach of 100 km
and beyond, a three thread implementation is the most suitable option to achieve the best
performance for the proposed EIS scheme. Here it is worth mentioning that the maximum
throughput can be slightly higher than 0.497 (Fig. 6) since the exact value for the offered
load is 0.495 under the high load scenario. Furthermore, packet loss can be minimized (or
eliminated) by employing a larger buffer at the ONUs, which may significantly degrade
the delay and jitter performance.
Figure 4. Packet Delay vs. Distance

14
Figure 5. Jitter vs. Distance
Figure 6. Throughput vs. Distance

15
6. CONCLUSIONS
Our approach tends to perform well, generating comparatively small abstract models using a
relatively large number of (small, local) refinement steps. When the number of formal abstract
models becomes particularly high, performance is degraded but, in our experiments, the tool still
outperformed the game-based abstraction of PRISM. This gain derives from the use of simple
operations on smaller abstractions and a reduction in the amount of numerical computation that
needs to be performed. Perhaps unsurprisingly, our approach performs better on real-time models,
than on the versions that have been discretised. We have presented a novel formal abstraction
approach for the performance analysis of probabilistic, real-time systems with potentially infinite
data variables. This approach uses local formal abstract steps, which results in more compact
abstractions than alternative abstraction refinement techniques.
The network operators have LR-PON exhibits tangible advantages in terms of cost savings and
hence have been identified as a promising candidate for future broadband access. One of the most
important challenges in LR-PON is to deal with the significant network performance degradation
because of the increased propagation delay. An efficient way to mitigate this performance
degradation has advocated multi-thread-based DBA approach. However, this article shows that
without a proper inter-communication mechanism among the overlapped bandwidth allocation
processes, the efficiency of a multi-thread DBA approach could be affected drastically. In this
regard, we concentrate on the multi-thread DBA approach, and highlight the issues arising due to
the lack of inter-thread scheduling. After making an assessment of the currently available
solutions, we have proposed a new approach named enhanced inter-thread scheduling (EIS),
which integrates key features from the existing inter-thread scheduling algorithms.
We pointed out some inaccuracies in the multi-thread allocation algorithm and suggested some
modifications to ensure that an ONU is not granted more than requested, by efficiently
distributing the excess bandwidth among heavily loaded ONUs, and also to enable enhanced
inter-thread scheduling to fully utilize a thread without disturbing the thread tuning. Simulation
results show that enhanced inter-thread polling succeeds in decreasing reporting and queuing
delays, whereas online inter-thread polling has a lower grant delay and therefore achieves a better
overall delay performance. Online inter-thread polling also achieves a higher throughput, since
multi-thread polling use more bandwidth for report messages and guard intervals.
REFERENCES
[1] Tony Tsang, “Performance Analysis for QoS-Aware Two-Layer Scheduling in LTE Networks”,
International Journal of Emerging Trends & Technology in Computer Science (IJETTCS), Vol. 2,
Issue 2, July-August 2013.
[2] Marta Kwiatkowska, Gethin Norman and David Parker, “PRISM 4.0: Verification of Probabilistic
Real-time Systems”, In Proceeding 23rd International Conference on Computer Aided Verification
(CAV’11), volume 6806 of Lecture Notes of computer Science, pages 585-591, Springer, July 2011.
[3] Song H., Kim B.W., and Mukherjee B., “Long-Reach Optical Access Networks: A Survey of
Research Challenges, Demonstrations, and Bandwidth Assignment Mechanisms”, IEEE
Communications Surveys & Tutorials, vol. 12, no. 1, pages 112-123, 2010
[4] Jensen, H.: “Model checking probabilistic real time systems”, In Proceeding 7th Nordic Workshop on
Programming Theory, Report 86, Chalmers University of Technology, pages 247-261, 1996.
[5] Kwiatkowska, M., Norman, G., Segala, R., Sproston, J., “Automatic verification of real-time systems
with discrete probability distributions”, Theoretical Computer Science (TCS)282, pages 101-150,
2002.
[6] Beauquier D., “Probabilistic timed automata”, Theoretical Computer Science (TCS)292(1), pages 65-
84, 2003.

16
[7] Clarke E., Emerson E., Sistla A., “Automatic verification of finite-state concurrent systems using
temporal logics”, ACM Transactions on Programming Languages and Systems 8 (2) pages 244V263,
1986.
[8] Alur R.,Courcoubetis C., Dill D., “Model checking in dense real time”, Information and Computation
104 (1) pages 2V34, 1993.
[9] Hansson H., Jonsson B., “A logic for reasoning about time and reliability”, Formal Aspects of
Computing 6 (4) pages 512V535, 1994.
[10] Song H., Kim B W.,, and B. Mukherjee B., “Multi-Thread Polling: A Dynamic Bandwidth
Distribution Scheme in Long-Reach PON”, IEEE Journal Selected Area Communications (JSAC),
vol. 27, pages 134-142, 2009
[11] Helmy A., Fathallah H., and Mouftah H., “Interleaved Polling Versus Multi-Thread Polling for
Bandwidth Allocation in Long-Reach PONs”, IEEE/OSA Journal Optical Communication and
Networks, vol. 4, no. 3, pages 210V18, March 2012.
[12] Skubic B. et al., “Dynamic Bandwidth Allocation for Long- Reach PON: Overcoming Performance
Degradation”, IEEE Communications Magazine, vol. 48, pages 100V108, Nov. 2010.
Authors
Tony Tsang received the BEng degree in Electronics & Electrical Engineering with First Class Honours
in U.K., in 1992. He received the Ph.D. from the La Trobe University (Australia) in 2000. He was
awarded the La Trobe University Post graduation Scholarship in 1998. He is a Lecturer at the Hong Kong
Polytechnic University. Prior to join in the Hong Kong Polytechnic University, Dr. Tsang earned several
years of teaching and researching experience in the Department of Computer Science and Computer
Engineering, La Trobe University. His research interests include mobile computing, networking, protocol
engineering and formal methods. Dr. Tsang is a member of the ACM and the IEEE.

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