Deterministic Lightpath Scheduling and Routing in Elastic Optical Networks

A huge torrent of data traffic is generated from various heterogeneous applications and services at the Internet backbone. In general, at the backbone, all such applications and services are allocated spectral resources under a shared spectrum environment within elastic optical networks (EONs). In such a fully shared environment, connection requests (CRs) belonging to different traffic profiles compete for spectral resources. Hence, it is very challenging for network operators to resolve resource conflict that occur at the time of provisioning resources to such CRs. The heterogeneous traffic profile (HTP) considered in this work includes permanent lightpath demands (PLDs) and scheduled lightpath demands (SLDs). We propose various distance adaptive routing and spectrum assignment (DA-RSA) heuristics to resolve resource conflict among these two traffic profiles in EONs under a full sharing environment. Conventionally, preemption was the only technique to resolve such resource conflict among HTPs. Since preemption involves the overhead of selecting CRs to be preempted and then deallocating the resources given to those CRs, excessive preemption adversely affects the performance of the network. Therefore, in this work, we utilized bandwidth splitting as a solution to resolve resource conflict among HTPs under such a shared environment in EONs. Moreover, an integrated solution consisting of splitting and preemption is also proposed. We refer to this new integration as flow-based preemption. Our simulation results demonstrate that bandwidth splitting-based heuristics yield significant improvement in terms of the amount of bandwidth accepted in the network, link and node utilization ratio, number of transponders utilized and the amount of bandwidth dropped due to preemption. Moreover, the flow-based preemption approach is proved to be superior in performance amongst all proposed strategies.


Introduction
There has been a surge of technological transition in the design and operation of optical networks. The ITU-T flex-grid, orthogonal frequency division multiplexing (OFDM), reconfigurable optical add-drop multiplexers (ROADMs), bandwidth variable transponders (BVTs) are now embraced by optical network operators. All these elements are inherent part of today's optical networks which are known as elastic optical networks (EONs) [1]. Due to the use of flex-grid, whole optical spectrum is perceived in terms of fine sized blocks which are known as frequency slots (FSs). Unlike traditional optical networks which were based on fixed-grid and utilizing wavelength division multiplexing (WDM) technique, the unique feature of EONs is that they are able to allocate just enough bandwidth to demands by allocating FSs according to characteristics (such as optical reach, optical path signal to noise ratio, etc.) of the optical path. This means EONs are able to transmit optical signals with the adaptive selection of modulation level on the basis of optical reach without needing signal regeneration. This distance-adaptive transmission makes EONs highly spectrum efficient and thus this kind of routing and spectrum assignment (RSA) [2] is referred to as distance adaptive RSA (DA-RSA) or routing, modulation level and spectrum assignment (RMLSA) in EONs [3,4].
EONs receive heterogeneous traffic emerging from various data intensive services (including cloud computing, big data analytics, image processing, etc.) which involve interand-intra data center transmissions to and from corporate giants, research organizations, etc. as well as the regular data traffic from domestic users. The inter-and-intra data center traffic involves very huge sized data streams called elephant flows. These elephant flows have very rigid quality of service (QoS) requirements which ensure guaranteed availability of resources. Hence, the request for such traffic flows is made to the network (operator) long before their actual transmission time. Thus, the network operator has a traffic matrix of such connection requests (CRs) ahead of time, indicating their setup time, tear down time and the amount of bandwidth needed. In optical networks, these CRs are known as scheduled lightpath demands (SLDs) [5,6]. There also exist certain data services which need to be served as and when they arrive and thus they do not have any stringent QoS requirements. The demand for such services are called as permanent lightpath demands (PLDs). Unlike SLDs, PLDs do not mention their timing information. PLDs are perceived as greedy in terms of occupying spectral resources; once arrived, they remain in the network as long as it is functional. Therefore, the traffic matrix of such CRs contains their source-destination (s-d) pair information along with their bandwidth requirement.
In an environment where spectrum is shared by such heterogeneous CRs, resource competition is very high and hence resource conflict will occur often. Preemption is a mechanism to resolve resource conflict in the presence of HTPs. In a shared spectrum environment, the provisioning of HTPs can either be preemptive (PR) or non-preemptive (NoPR). In PR provisioning, whenever a resource conflict arises in the network, low priority CR relinquishes control over resources and high priority CRs are provisioned on those resources. This is called disruption or preemption of low priority CRs. In contrast to PR, in NoPR provisioning, CRs are served as they arrive. Excessive preemption is hazardous to CRs which are preempted due to resource conflict. Hence whenever, PR provisioning is performed, measures have to be taken to minimize such preemption in the network.
In this work, we model deterministic lightpath scheduling (DLS) problem in EONs to resolve challenges that arise due to resource conflicts at the time of provisioning resources to HTPs. The DLS problem is deterministic in nature, i.e., it includes the traffic profiles in which complete traffic matrix is given beforehand. Thus, the DLS problem can be viewed as a variant of static resource planning problem which constitutes a mix of traffic profiles. The aim of DLS problem is to increase the amount of bandwidth accommodated in the network and maintain an efficient utilization of spectral resources. Previous work on provisioning heterogeneous traffic specifically with two traffic profiles in EONs has been presented in [7][8][9][10][11][12][13]. However, to the best of our knowledge, the work presented in this paper is the first attempt to solve DLS problem in the context of EONs.
We propose four DA-RSA heuristics for EONs with the objective of accommodating a high volume of bandwidth in the network thereby utilizing spectral resources efficiently in order to address DLS problem. We refer to these heuristics as heterogeneous DA-RSA (HDAR), preemptive HDAR (PHDAR), integrated HDAR with splitting and preemption (IHDAR), split HDAR (SHDAR). Our proposed heuristics utilize both NoPR as well as PR provisioning. Initially, SLDs and PLDs are served without performing preemption. Next, we observe the impact of PR provisioning on the network in the presence of SLDs and PLDs. Afterwards, we utilize bandwidth splitting [5] and preemption together to reduce preemption of PLDs. The SLDs are split with respect to their bandwidth in multiple chunks. Simulation results demonstrate superior performance in this case even with the single path routing, which eliminates the need for utilizing complex multipath routing. To further access the potential of splitting SLDs in alleviating the resource conflicts, we utilized bandwidth splitting instead of preemption of PLDs, in another heuristic. On evaluating the results of these heuristics, it is revealed that when splitting and preemption are used simultaneously, the best performance is achieved. Thus, through this work it is demonstrated that in EONs splitting could be used to resolve resource conflict among HTPs and eliminate the need of utilizing preemption in the presence of heterogeneous traffic thereby avoiding the need to disrupt demands.
The remaining part of this paper is structured as follows: Sect. 2 reviews the previous work on SLDs, various kinds of static and dynamic HTPs and provisioning of HTPs in EONs. In Sect. 3, system model and the proposed heuristics are discussed. Section 4 describes the simulation scenario and presents the analysis of results obtained. Finally, Sect. 5 concludes the paper.

Literature Review
The concept of SLDs was originally presented by Kuri et al. in [14] with reference to conventional WDM optical networks. In [15] authors categorized PLDs and SLDs as static immediate reservation (IR) and static advance reservation (AR) requests, respectively. The readers are requested to refer [15] to understand more on PLDs and SLDs in detail. The concept of SLDs is relatively new to EONs and it has been discussed in [5,6]. Authors in [5], utilized the knowledge of spatial and temporal dimension of SLDs to ease the provisioning of voluminous SLDs. They have proposed several RSA strategies in which the bandwidth of SLDs is split into a number of chunks and then routed using either single/ multi-path routing. In [6] authors proposed various RSA strategies and addressed the problem of spectrum fragmentation in EONs by considering scheduled traffic and dynamic traffic scenarios separately. In [5,14] authors did not consider HTPs. Though authors in [6] considered two traffic profiles in their work, they proposed different strategies to serve both the profiles, individually.
In [7] authors proposed a two-dimensional resource model and addressed the issue of spectrum and time fragmentation in EONs. Their proposed algorithm performs DA-RSA for CRs and meanwhile, if any of the AR requests are blocked, the already scheduled ARs (which are not in service) are re-optimized. Authors in [8] classified the spectral resources on the basis of the number of FSs required by CRs to reduce the spectrum fragmentation. The whole spectrum is divided into two prioritized areas: one to accommodate only IRs and other for both IRs and ARs. The border of the prioritized areas is flexible and can be adjusted to control the blocking of AR and IRs. The issue is addressed for multi-fiber EONs. In addition to AR and IR, authors in [9] proposed a weight based RSA heuristic to serve malleable reservation (MR) CRs in EONs. Though they considered a network with such HTPs, they did not observe the effect of these traffic profiles on each other.
In [10] authors proposed various RSA heuristics to reduce spectrum fragmentation and provide a mechanism to control the service level of both IR and AR requests. Instead of OFDM-based EONs authors considered space division multiplexing (SDM) based EON for this study. They have restricted AR requests to use a fixed path routing and allowed IR requests to select the best route among the k-shortest paths available in order to reduce the degradation in IR services. Their proposed strategy does not address the issue of preemption explicitly. In [11] both the proactive and reactive schemes to reduce IR service failures have been presented. In addition to preemption, the IR service failure in their work refers to the blocking of IR services. Authors have tailored the provisioning scheme as per the traffic intensity levels of IR and AR requests. Their proposed reactive scheme allowed reconfiguration of IRs. In EONs, under a dynamic environment, as the CRs come and depart, the issue of spectrum fragmentation arises. Another DA-RSA approach is proposed in [12] wherein authors have utilized splitting, and divided the AR and IR requests in smaller chunks and performed multipath routing to route those chunks. Authors in [13] have utilized preemption while performing QoS aware RSA to reduce the blocking probability of high priority requests. Though their heuristics utilized bandwidth squeezing and fragmentation, and utilized preemption whenever required.
Although there is a very small footprint found in EONs with respect to the provisioning of HTPs, we observed the following: none of the works have considered static HTPs, high priority CRs have been the focus throughout the work and negligence towards the significance of low priority traffic. Hence, degradation of low priority traffic has been there to a great extent. Moreover, the work presented in [9] did not touch upon resolving the resource conflict and preemption. The authors also assumed that IRs announce their service duration which does not happen in a real scenario. The work in [13] has a mention on preemption but the proposal lacks details about how they have selected CRs for preemption and how it has been performed.
The motivation for this work is the result of the fact that low priority requests cannot be ignored at the time of provisioning. The provisioning of HTPs is a real challenge in a shared environment as HTPs compete for resources thereby triggering resource conflict in the network. Preemption of low priority CRs should be performed consciously and it should be kept very low in order to preserve the throughput of the network. In this work, we are focusing on the static HTPs including SLDs and PLDs with the aim to accommodate more bandwidth in the network while reducing the preemption of PLDs in the network. Here, SLDs are considered as primary traffic and thus contrary to the works present in literature, the work assumed that the network traffic is dominated by high priority traffic profiles (i.e., SLDs). Also, conforming to the real scenario, PLDs in this work, are not supposed to announce their service time information. Moreover, to resolve the resource conflict and reduce preemption in the network, bandwidth splitting is employed in two ways: first it is informed in PR scenario and later in NoPR scenario. In both the cases, the proposed algorithms perform only single-path routing and save the operator from the complex computations of multi-path routing.

Provisioning of Heterogeneous Traffic Profiles (HTPs)
This section describes the nomenclature, constraints and design metrics used in this work. The subsections cover detailed discussion on the proposed heuristics.
A weighted undirected graph G(N, L, , F) is used to describe the physical network topology where, N is the set of nodes, L is the set of bidirectional links adjoining the nodes, weight function ∶ L → ℝ + which maps the physical length of the links between the nodes in the network and F is the set of FSs on each fiber link l ∈ L . A set of CRs  [5]. If it is a PLD then i denotes the arrival time, and in this case, the value of i becomes insignificant as the PLD does not mention its tear down time. We assume that the time is slotted and the duration for each time slot is set to one hour. A set T is used to indicate the set of time slots such that |T| = 24 . Thus, in simulations, to differentiate between SLDs and PLDs, we set i > 24 for PLDs. In this work, we use k-shortest path routing algorithm with k = 3 . The set of candidate paths corresponding to R i is denoted by a set K . These k-candidate paths are precomputed corresponding to each CR present in set R.
Since EON is equipped with (S)BVTs, we use the set BV to represent the transponders on a node. The capacity of a transponder b ∈ BV is denoted by TCap b (in Gbps) and TCUtil b indicates the utilized capacity of a transponder (in Gbps) b ∈ BV . A variable TSP n represents the number of (S)BVTs present on n ∈ N . We assume that SBVT is logically divided into a number of sub-transponders (S-TSPs) and each S-TSP is assumed to be a low-capacity BVT. The variable S is used to represent the number of S-TSPs that belong to an SBVT which is bounded by the value of TCap b . That is, the number of S-TSPs belonging to an SBVT should not exceed the total capacity of a SBVT. For this work we assumed it to be 1 ≤ S ≤ 4 [5]. If b ∈ BV is a BVT then S = 1 . If b ∈ BV is an SBVT then TCap bn indicates the total capacity of a transponder on node n ∈ N . If the (S)BVT b ∈ BV is utilized on node n ∈ N , the value of boolean variable NTSP nb is set to 1, otherwise 0. In a non-grooming environment, a BVT can be utilized by only one CR at a time instant; therefore, if NTSP nb = 1 for a BVT b ∈ BV then TCUtil b = TCap b . The total capacity of transponders utilized on a node is given by, The proposed PHDAR and IHDAR heuristics perform preemptive provisioning thereby allowing preemption of PLDs. The vector PLD DB keeps track of candidate PLDs for preemption. A candidate PLD is such a PLD, with which the current SLD is facing resource conflict. Candidate PLDs are preempted when SLD does not find resources on any of the candidate paths from set K . A boolean variable Req ip is set to 1 for a PLD if it is preempted, otherwise 0. If a CR R i is accepted then the value of variable A i is set to 1, else 0. In SHDAR and IHDAR heuristics, bandwidth splitting of SLDs is performed and the flows belonging to a SLD are allowed to route by using single-path routing only. In order to perform splitting, these two heuristics modified the splitting model that we designed in [5]. Contrary to [5], in this work we performed DA-RSA for HTPs and did not perform multi-path routing. Due to this, the mathematical formulations have been revised. We consider four modulation formats (i.e., BPSK, QPSK, 8-QAM and 16-QAM). The values of spectrum efficiency (SE) corresponding to BPSK, QPSK, 8-QAM and 16-QAM are 1, 2, 3 and 4 bits/s/Hz, respectively.
The following constraints should hold: (i) Since the heuristics are performing DA-RSA, spectrum continuity and contiguity constraints should hold. (ii) A FS on a link cannot be allocated to either a SLD or a PLD simultaneously, or two SLDs at a time instant. This means, they are not allowed to use a single spectral resource during a time slot. This implies that a PLD can utilize a FS with SLD, only if its arrival time ( ) is greater than the tear down time ( ) of a SLD, whereas the same FS can be allocated to two SLDs if both of them are disjoint in time. This is known as time-disjointness property of SLDs [5]. (iii) A CR is allowed to be preempted only if it is a PLD. Moreover, a PLD cannot be preempted by other PLD. That means, only SLDs are allowed to preempt PLDs if they could not be allocated their desired number of FSs on a route.

Heterogeneous Distance Adaptive Routing and Spectrum Assignment (HDAR) Heuristic
We introduced HDAR heuristic in order to perform DA-RSA for the heterogeneous traffic profiles (i.e., SLDs and PLDs) in EONs. HDAR performs NoPR provisioning of SLDs and PLDs within a full-sharing framework. A traffic matrix in the form of set R is given, which is a mix of SLDs and PLDs. These CRs are entering into the network as a tuple mentioned earlier in this section. As a CR enters into the network, HDAR first checks the value of tear down time, to know whether it is a PLD or SLD. If > 24 , then CR is identified as PLD, else SLD. Next, it selects the route from available k-candidate paths. Now, according to length of the route, HDAR selects appropriate modulation levels and converts the bandwidth into FSs. This is done in accordance to the value of spectrum efficiency ( SE) corresponding to the modulation format, as follows: where, RFS i , Slot w and GB indicate the number of requested FSs, width of a FSs (in GHz) and the number of guard bands required, respectively. Next, the desired number of FSs (i.e., RFS) are searched for this CR.
HDAR provisions PLDs as they arrive, and schedules SLDs in the network so that they use network resources during their respective setup times. The route, modulation format and the spectrum, all are assigned to a CR only if it satisfies all the constraints mentioned earlier in this section. (2)

Preemptive Heterogeneous Distance Adaptive Routing and Spectrum Assignment (PHDAR) Heuristic
Unlike HDAR, PHDAR performs PR provisioning of HTPs in this work. At the time of serving PLDs, PHDAR performs similar to HDAR. However, when a SLD arrives, the heuristic starts collecting information about PLDs that are coming across this SLD at the time of performing DA-RSA. If the SLD could not find resources on a route, then all the collected PLDs now become a set of candidate PLDs to be preempted, for this SLD. That is, by preempting one or more PLDs from this set of candidate PLDs, the SLD could be served. In order to select the candidate PLD from among the set, PHDAR first sorts all the PLDs in the set in ascending order of the number of FSs allocated to them. Next, PHDAR sequentially selects a PLD from this sorted list and preempt it by de-allocating the resources occupied by this PLD and again perform DA-RSA for this SLD considering the recently de-allocated resources. Now, if RSA is not successful then PHDAR selects next PLD from the list and repeat the process until the SLD could be accepted in the network.

Integrated Heterogeneous Distance Adaptive Routing and Spectrum Assignment with Splitting and Preemption (IHDAR) Heuristic
Resolving resource competition in a shared environment is a challenging task in the network as it involves preemption of some PLDs. Moreover, preemption has an adverse impact on the performance of network as it involves identification of potential preemption candidates and then deallocating resources for those CRs. In addition to this, the use of SBVTs in EONs has increased its potential to meet diverse requirements of customers. Therefore, here we propose to utilize bandwidth splitting and preemption in a single heuristic for the first time in EON to resolve resource conflicts and to reduce preemption of PLDs. Whenever a route with desired number of FSs is not found for a SLD, before preempting any PLD, IHDAR first attempts to serve such SLD by splitting its bandwidth into multiple chunks, referred to as flows; and then considers each flow as an independent SLD. Next, IHDAR performs DA-RSA for each flow. Similar to PHDAR, at this level, IHDAR starts collecting the information about PLDs and maintains a set of candidate PLDs corresponding to each flow. Now, if any of the flow is not able to avail the resources then IHDAR performs preemption of PLDs in a manner similar to PHDAR. Thus, IHDAR performs splitting at flow level thereby reducing the number of preemptions caused due to SLDs in the network. IHDAR has a tuning parameter which is used at the time of computing flow threshold F th . Here the flow threshold is computed as follows: Where, RB denotes the mean bandwidth requested by all CRs. Here may take values such that 1 ≤ ≤ 4 . On the basis of this F th , IHDAR decides that in how many flows a SLD can be split. The variable NFlow i is used to indicate the number of flows in which a SLD R i is split. A SLD cannot split into more than S flows i.e., ( NFlow i ≤ S ). Thus, F th balances the value of NFlow i by tuning the value of . NFlow i is computed as follows:

The size of each flow is represented by a variable SFlow i,j is defined as
The algorithm for IHDAR is presented in Table 1. It shows how IHDAR performs flowbased preemption.

Split Heterogeneous Distance Adaptive Routing and Spectrum Assignment (SHDAR) Heuristic
In order to see the effect of splitting on HTPs, we propose a NoPR version of IHDAR in the form of SHDAR. Thus, SHDAR employs only splitting with the aim of improving network performance in the presence of HTPs. It performs splitting of SLDs only whenever DA-RSA is unsuccessful on a particular route for a SLD. Here, the splitting process is similar to that of IHDAR. This means, multiple chunks belonging to a SLD are routed using single-path routing. This allowed us to see the benefits that the splitting process has brought to the network.

Performance Evaluation
This section presents the simulation assumptions and discusses the results obtained from simulations to evaluate the performance of proposed heuristics.

Simulation Assumptions
We evaluate the proposed algorithms by performing simulations in MATLAB using NSFNET as shown in Fig. 1. We assume EON with 4 THz spectrum where the spectral width of each FS is 12.5 GHz. Thus, there are 320 FSs in the spectrum. We assume each node in the network is equipped with infinite (S)BVTs, each of which is capable to support the data rates up to 400 Gbps. Each SBVT is further divided into 4 S-TSPs. The line rates required by CRs are assumed to be 25, 75, 125, 150, 200 and 250 Gbps and are uniformly distributed among all CRs in the set R . The transmission distance corresponding to the four modulation formats are 9600, 4800, 2400 and 1200 km for BPSK, QPSK, 8QAM and 16QAM, respectively [16]. First-fit spectrum allocation technique is used under a fully shared spectrum in all the proposed heuristics. The HTP is a mix of SLDs and PLDs which are considered in the ratio of 6:4 for the purpose of performance evaluation as we assumed that due to the rise of bandwidth intensive rigid QoS services, there will be more number of SLDs than PLDs in the network. The setup and tear down times for SLDs and the arrival time for PLDs are generated randomly along with the specific line rates required by them. The CRs present in set R are varied at each simulation run and the results presented in the following sub-section are averaged over 10 simulation runs.

Results and Discussion
Since this is the first work concerning static HTPs (i.e., PLDs and SLDs), we consider HDAR as the benchmark to evaluate the performance of the proposed heuristics. HDAR does not employ any spectral resource conflict mechanism and thus becomes suitable candidate as a benchmark to evaluate the benefits achieved by the proposed conflict resolution heuristics. In case of SHDAR and IHDAR, we have performed simulations for three different values (i.e., 1, 2 and 4) of ω. This value is the crucial factor in deciding the F th as indicated in Table 1. The results reported in this section are with = 4 . Figure 2 indicates the amount of bandwidth accepted (in Tbps) corresponding to all the heuristics. At low load (i.e., < 800 CRs), performance of all the strategies is same. However, as load increases, the gap between HDAR and other proposed heuristics grows significantly. The most and least gain achieved by the proposed heuristics are 26.72% and 10.78% in case of IHDAR and PHDAR, respectively for the metric under consideration. All heuristics except HDAR employed resource conflict resolution mechanism(s). This highlights the importance of resolving the resource conflict when there are HTPs present in the network. IHDAR and SHDAR accepted 14.38% and 7.84% more bandwidth in the network than PHDAR. This is because whenever a SLD is getting blocked in PHDAR, it preempted more number of PLDs, indicating the inefficiency of PHDAR in utilizing preemption efficiently. Excessive preemption leads to generate more number of fragments when the arriving SLD is not utilizing all the FSs emptied by the candidate PLD(s). IHDAR accepted maximum bandwidth because it achieved a good balance between splitting and preemption by performing flowbased preemption. The graph shown in Fig. 3 illustrates the link utilization ratio (LUR). This is defined as the ratio of the number of FSs consumed to the number of CRs accepted in the The percentage decrease in LUR between HDAR and PHDAR is 24.19% which is further decreased to 15.09% when the network is heavily loaded. The rate of LUR decrease is highest in HDAR and lowest in case of IHDAR and SHDAR. This is because HDAR does not differentiate among the two traffic profiles, and this results in consuming more FSs even for accepting fewer CRs in contrast to IHDAR and SHDAR. Figure 4 depicts the node utilization ratio (NUR) versus the number of CRs arriving into the network. The NUR which represents ratio of the total (S)BVTs utilized to the amount of bandwidth accepted in the network. At high load, PHDAR achieved nearly same performance as IHDAR and SHDAR. This is because as CRs increase in the network, (S)BVTs are exhausted. Therefore, only SLDs are accepted because they can utilize the same SBVTs if the time-disjointness constraint is satisfied. The graph shown in Fig. 5 represents the total number of transponders (TSPs i.e., (S) BVTs) utilized as the CRs arrive in the network. The rate of growth of this curve indicates the amount of CRs accommodated in the network. HDAR has utilized maximum number of TSPs even when the network is lightly loaded whereas in case of IHDAR and SHDAR, the TSPs present in the network are exhausted when the network is heavily loaded. However, PHDAR utilized maximum number of TSPs at a relatively moderate traffic load. At peak load all of the strategies have utilized maximum TSPs available in the network.
The two of the proposed heuristics (i.e., PHDAR and IHDAR) have utilized preemption as the resource conflict resolution technique. The graph presented in Fig. 6 depicts the amount of bandwidth dropped due to preemption of PLDs in both the heuristics. When the traffic load is approximately 810 CRs, both heuristics did not need to utilize preemption to accommodate SLDs in the network. As the number of CRs grew from this point, PHDAR started preempting PLDs which resulted in an increase in the amount of The amount of bandwidth dropped (in Tbps) with respect to the number of connection requests arrived in the network bandwidth dropped in the network. Although IHDAR also preempted PLDs but the rate at which the bandwidth is dropped in the network is very low; thus, it has dropped 13.32% less bandwidth than PHDAR. This is due to the fact that PHDAR employed preemption excessively by dropping more number of PLDs to accommodate every SLD. However, utilizing splitting and preemption together to perform flow-based preemption saves on excessive preemption and hence it drops very small amount of bandwidth.
It is evident from the graphs shown in Figs. 2, 3, 4, 5 that IHDAR and SHDAR both have outperformed HDAR and PHDAR. Table 2 reaffirms this fact again with respect to the number of FSs utilized and the number of spectral fragments generated in the process of DA-RSA by all the heuristics. The reason for the two heuristics (IHDAR and SHDAR) to have similar performance is again highlighted in the table. Both the heuristics have a minute gap in terms of number of CRs accepted. Although the number of FSs utilized by SHDAR is more, it has generated less number of fragments in the spectrum as compared to IHDAR.
From the simulation experiments it is clear that resolving resource conflicts when there are HTPs in the network, is essential to achieve good performance from the network. Amongst all the heuristics, PHDAR, IHDAR and SHDAR employed either preemption, splitting or both as the conflict resolution technique(s), the results reveal that both IHDAR and SHDAR outperformed PHDAR. This affirms that only utilizing conflict resolution technique alone is not enough; a heuristic must utilize them intelligently in order to avoid the adverse effects caused by excessive preemption and splitting.

Conclusion
In this paper, various DA-RSA heuristics are proposed in order to perform deterministic lightpath routing and scheduling of HTPs. Conventionally, preemption was the only technique which was used in the full sharing environment to resolve the resource conflict among various traffic profiles. In this work, we proposed to utilize splitting, and splitting with preemption for this purpose under a full sharing framework in EONs. The proposed heuristics employing splitting have demonstrated superior performance by routing all flows pertaining to a CR via single-path only. Thus, IHDAR and SHDAR are free from the complexities that are otherwise involved when multi-path routing is used. It is important to resolve resource conflict when HTPs are present in a fully shared environment. Therefore, in this work, we have utilized splitting as a tool to resolve resource conflict and avoid preemption of PLDs. Simulation results point out that though the number of fragments generated are more in flow-based preemption under IHDAR; it outperformed on all other metrics of interest and thus it is more effective than those heuristics in which splitting or preemption has been used in isolation. The work presented in this manuscript is focused on full sharing spectrum framework. In future, the effect of other spectrum sharing frameworks such as strict partitioning and flexible partitioning could be studied on HTPs.