Holding-Time Information (HTI): When to Use it?

Holding-Time Information (HTI): When to Use it? Sandeep Kumar Singh and Admela Jukan Technische Universit¨at Carolo-Wilhelmina zu Braunschweig, Germany {sandeep.singh, a.jukan}@tu-bs.de

Abstract: The known technique of HTI-aware routing can be used for connection admission, or spectrum defragmentation. We show that HTI used for defragmentation is the most beneficial in reducing blocking in space-division multiplexed elastic optical networks. OCIS codes: (060.4251) Networks, assignment and routing algorithms; (060.4264) Networks, wavelength assignment.

1.

Introduction

Space-division multiplexing (SDM) – realized by multicore/multimode fibers in elastic optical networks (EONs) – has emerged as a viable networking solution for offering flexible and large bandwidth. Despite multiple dimensions in resource allocation, also SDM networks are however prone to spectrum fragmentation [1]. Spectrum fragmentation can be addressed either in the connection admission phase, or on-demand spectrum defragmentation (DF) via reconfigurations [2]. The known technique of holding-time information (HTI)-aware routing can be used in both cases, i.e., for connection admission, or spectrum defragmentation [3]. When to best use HTI, however – whether in connection admission or on-demand defragmentation, is an open question. To answer this, we first observe that HTI for most modern applications (in data centers) is not known in advance, and is heavy-tailed distributed [4]. Especially the admission control with an estimated HTI can be inaccurate at the connection setup time. To this end, we propose to study how and when to use the HTI: whether for routing, spectrum and core allocation (RSCA) in SDM-EONs that typically considers an inaccurate estimate of HTI, or during reconfiguration of connections in a DF scheme. Although HTI can be utilized in a DF scheme to consolidate scattered free spectrum, an advantage of using HTI in reducing fragmentation during connection admission phase (RSCA) is that it does not require to reconfigure active connections, and hence avoids any service interruption. The results show though that the best way of using HTI is in for on-demand defragmentation, while keeping the admission control simple.

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2. HTI-aware Connection Admission and Defragmentation Schemes Let us first consider an example in Fig. 1 to explain the RSCA with HTI as described in Algorithm 1. Fig. 1(a) shows the spectrum occupancy of connections in a 2-core fiber-link when a new request C5 arrives with demand of 2 consecutive slots. The request C5 can be established over a spectrum path (SP) with slots [2, 3] in a core 1 or {[3, 4] or [4, 5]} in a core 2. The remaining lifetimes of established connections together with the two ([2, 3] and [3, 4]) of three possible spectrum assignments for the request C5 in a block B1 and B2 of core 1 and 2, respectively is depicted in Fig. 1(b). To select the best possible SP with the aim of minimizing fragmentation, we propose a link fragmentation index (FI) for an SP i, which is associated with its neighboring connections in a block Bi , in Eq. (i) in Fig. 1(c). The link FI of an SP (φ l (spi )) utilizes the remaining lifetimes of an incoming request and its neighboring connections along the

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Fig. 1. (a) Spectrum occupancy in a 2-core fiber with 5 slots each. (b) The remaining lifetimes of connections together with a new request C5 . (c) A fragmentation metric with HTI and a cost function.

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Algorithm 1 HTI-aware Connection Admission (HTI-CA) Scheme [Given: Arriving request C(s, d, b, h)] 1: Find all SPs on all cores, or allowed cores in case of priority, of a shortest fiber-level path between a sourcedestination (s − d) pair that can satisfy a new request C with demand b consecutive slots and holding time h. 2: Assign costs to all SPs as in Eq. (ii) in Fig. 1(c), and select a minimum cost SP to allocate spectrum to request C. SP. Note that the remaining lifetime of a new request is same as its holding time h (or mean remaining lifetimes, MRL ¯ when HTI is unknown). However, for its neighboring connections, MRLs depend on how long they are active, i.e. h, t − tsi , where t is the current time and tsi is the setup time for a connection Ci . For example, an FI φ l (sp1 ) is calculated as the ratio of the average value of differential remaining lifetimes of left (τL1 ), center (i.e., incoming, τC1 ) and right (τR1 = 0) connections C1 ,C5 and C2 respectively, and the maximum value of these TB1 = max(τL1 , τC1 , τR1 ) in the block B1 . It should be noted that when the spectrum is free to the left or right of an SP i, then τLi or τRi is considered as 1, as shown in a block B2 in Fig. 1(b). This ensures that φ (spi ) is minimum for those SPs that fits into the gap between two established connections, as well as the incoming request will depart together with its neighbors. In Algorithm 1, a minimum cost SP is selected for an incoming request using Eq. (ii), which sums FI on each link traversed by the SP. As mentioned before, most applications do not have HTI in advance during connection admission phase and its estimation (MRL) might not be accurate at connection setup time, the HTI (or MRL) is best suitable to be utilized during the reconfiguration of connections. For this purpose, we propose a DF reconfiguration scheme in Algorithm 2 that prefers to allocate an incoming request C between a source-destination (s − d) node-pair along with other existing s−d connections, at the time of connection admission procedure. It should be noted that this process is triggered by the connection request, but uses a simple RSCA (like first fit, without consideration of HTI) and a separate defragmentation process that considers HTI. When it is not possible to allocate the new request C along other s − d connections, then we try to find a first available SP on a core to route this request. However, we reallocate some connections within the same core, where they are established, or in different cores, when the request C cannot be admitted normally due to spectrum fragmentation. It should be noted that when connections are allowed to be reconfigured only within the same core where they are currently assigned, it will minimize the reconfiguration complexity and time. In Algorithm 2, it is preferred to set free spectrum window currently occupied by connections adjacent to other s − d connections such that a new s − d request can be routed along other s − d connections. This helps in two ways: first, routing all s − d connections adjacent to each other minimizes spectrum fragmentation; and second, the adjacent s − d connections can be reconfigured easily without any service disruption [3] in a decreasing order of their remaining lifetimes, which is calculated as h − (t − tsi ) for known HTI (h) or estimated (MRL) when HTI is unknown for each connection Ci . This ensures that the spectrum will remain in a non-fragmented state for longer time, and thus will result in lower blocking. 3. Performance Evaluation We present the simulation results to evaluate the performance of both methods: RSCA and DF with HTI for a NSFnet topology with 14-node and 21 fiber-links, each with 5 cores and each core with 100 spectrum slots. We consider three types of requests with demands 1, 2 and 8 consecutive slots. The requests are generated with exponential interarrivals for each uniformly selected source-destination (s − d) node pair. The traffic load is calculated as ∑∀s−d λs−d /µ, where λs−d is the mean arrival rate between s − d node pair, and 1/µ is the average service (holding) time of connections. The arrival rates of requests are proportional to the number of ports, which is in the ratio of 8 : 4 : 1. The holding times of the requests are lognormally distributed with mean 1/µ=10 time units and coefficient of variation (CoV) as 1 and 5 for two different scenarios. If the holding time is not known for any connection, then we calculate its mean residual lifetime, which is a function of the already served time, i.e., the traffic history. For the case of core-priority, we divided 5 cores among requests as [i, 4, 5] for a class i, where i = 1, 2, and 3, i.e., core 4 and 5 are shared among all 3 classes. Fig. 2(a) presents bandwidth blocking ratio (BBR), defined as ratio of blocked bandwidth demands to offered demands, with CoV=1 for our HTI-CA and HTI-DF schemes, as well as a priority-based core assignment scheme [1] against the first-fit (FF) policy which assigns first available SP to a new request. When reconfiguration of connections Algorithm 2 HTI-aware Defragmentation (HTI-DF) Scheme [Given: Arriving request C(s, d, b, h)] 1: Find an SP on a first available core of a shortest fiber-level path along with other connections between s − d pair to allocate spectrum to C. Otherwise, apply an RSCA scheme (e.g., first-fit) to find an SP to admit the request C. 2: If the request is not admitted, reallocate connections from spectrum window [i, i + b − 1] to other slots on the allowed cores using a maximal independent set-based scheme in [2] such that b slots can be set free for C. 3: Repeat previous step until the request C is established: first for each spectrum index i such that i or i + b − 1 is adjacent to spectrum index occupied by an s − d connection, and then for the remaining index i. 4: Reconfigure adjacent s − d connections in a decreasing order of their remaining lifetimes.

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Fig. 2. Effect of HTI on RSCA and DF schemes: (a) BBR at CoV=1, (b) percentage blocking reduction, (c) BBR at CoV=5, and (d) number of connections reconfigured per defragmentation. is allowed (DF) in the network, it admits highest number of connections, irrespective of the percentage of connections with known HTI, as blocking is minimum in this case. On the other hand, HTI-CA method exhibits lower blocking than other RSCA schemes, when HTI of connections is known. On the other hand, when the percentage of connections with known HTI decreases, BBR increases because estimated HTI is not very accurate at the connection setup time, but it is still lower than FF at lower loads, which can be seen clearly in Fig. 2(b), where we plot percentage blocking reduction of our schemes as compare to the FF. FF method with priority-based core assignment has also positive gain at lower loads. However, unlike the HTI-DF scheme, the performance of RSCA schemes deteriorates at higher loads. To see the effect of traffic history (or MRL), we evaluate the performance of our schemes by setting CoV of lognormally distributed holding time as 5 and keeping the mean holing time fixed. In Fig. 2(c), we see the similar trend: HTI-CA scheme performs better when holding times of connections are completely known (100 %), and performance deteriorates with the decrease in the percentage of connections with known holding times (0 %). Moreover, HTI-aware DF reduces the blocking significantly, even though reconfiguration of connections are restricted to same (1) core where they are currently allocated. Blocking is lowest when connections are allowed to be reconfigured to all 5 cores. The reason is that the possibility of admitting a request, which will be blocked otherwise, by reconfiguration of some connections increases with more number of allowed cores. In Fig. 2(d), we plot the average number of connections reconfigured during each defragmentation. As expected, the average number of reconfigurations is highest when there is no restriction on the maximum number of connections to be reconfigured, and is lowest for the case that maximum number of reconfigurations is limited to 5 and allowed within the same core. For all the DF scenarios, it increases at first and then decreases with the increase in load, since at a larger load spectrum is mostly occupied. In summary, HTI is an important parameter to be used for both RSCA and DF, however, when network operator allows a certain number of connections’ reconfigurations, then a simple and effective spectrum allocation used in our DF scheme that utilizes the HTI or MRL of connections is recommended rather than using a complex HTI-based RSCA. 4. Conclusion We proposed an HTI-aware connection admission scheme, and a defragmentation scheme, and showed that an HTIaware DF scheme with a few reconfigurations is the most beneficial in reducing connection blocking in SDM-EONs. References 1. 2. 3. 4.

H. Tode et al., “Routing, spectrum and core assignment on SDM optical networks (Invited),” OFC 2016 Tu2H.1. Y. Yin et al. “Dynamic on-demand defragmentation in flexible bandwidth EONs.” Optics Express 2012. S. K. Singh et al., “Non-Disruptive Spectrum Defragmentation with HTA in Optical Networks,” ONDM 2016. T. Benson et al., “Network traffic characteristics of data centers in the wild,” SIGCOMM 2010, pp. 202–208.