A novel hybrid data center architecture employing optically-switched WDM LANs over electrical fat trees

Inter connection network in a data center is the need of the hour as the communication backbone which caters the demands to accommodate a large number of servers with minimum possible end-to-end delay. The traditional Fat tree based topologies play a pivotal role for data center network (DCN) albeit in a low scale, on the other hand the upcoming electrical-cum-optical hybrid architecture demands huge power consumption and exhibit significant end-to-end delay. The present work depicts a proposal of highly scalable novel hybrid architecture employing optically switched WDM LANs (based on ShuffleNet topology) over electrical Fat trees with the use of substantial number of optical devices, the proposed DCN architecture is shown to offer reasonable reduction of end-to-end delay to 12.29 µs for mouse traffic and 10.01 ms for elephant traffic as compared to Optical Switching Architecture (OSA), which has significant 23 ms of delay for any traffic condition.


Introduction
In the age of cloud computing, where computation and storage continue to be pushed away from desktop, Data Centers (DC) from the major infrastructure, offering large scale utility service rendering from science to society (Cisco global cloud index: Forecast and methodology 2014-2019 2015). In response to the continually growing demands, DCs are being designed on a centralized and controlled setting to accommodate a large number of inter connected servers, such interconnections of huge number of servers on DCs are referred to as data center network (DCN). DCNs are expected to be flexible and reconfigurable to adopt rapidly altering demands on applications and service requirements (Greenberg et al. 2009a;Armbrust et al. 2009).
The DCN, in particular, desires to be flexible and reconfigurable to adapt rapidly to altering demands on applications and service requirements. Thus to improve the efficiency of the DCs, significant research has been done on designing improved architectures for the DCN.
The architecture and principle of operation of DCN differs from the traditional networks such as LAN and WAN. The primitive DCN architecture employed electrically-switched hierarchical architecture to accommodate limited number of servers and do not scale up to support additional servers. The improvision made through the use of optical systems and switching technique to ameliorate the issues like oversubscribed system, higher data rate over long distance transmission etc. and support on request availability (Zhang et al. 2011). In addition, optical switches are more energy efficient than the electrical ones, bringing about lower heat dissemination and less expensive cooling cost.
The main drawback in contemporary DCs is the measure of their energy efficiency. Typically during peak network load or busy hour DCNs are tuned for optimum efficiency and thus are extremely hungry for energy. It has been observed that a typical DCN facility features a power density of over a hundred times that of an office building in the same locality (Fehratovic and Aleksic 2010). Thus the DCN design structure and energy efficiency are the two reticular issues in a network.
The use of optical systems and switching technique relatively reduces the power consumption as compared to its electrical counterpart and at the same time end-to-end delay is also reduced. Hence in this paper, a novel Electrical-Optical Hybrid architecture is presented based on WDM technology to with substantial low latency. The rest of the paper is arranged as follows: In Sect. 2 a brief review on DCN topology has been made, the hybrid E-O architecture is proposed in Sect. 3, the detailed end-to-end delay analysis has been presented in Sect. 4 and the paper is concluded in Sect. 5 with a direction to future work.

Data center network topologies
Topology of the DC refers to the general construction of a DC. Communications networks also support DCs that assist in aggregating information and enabling them to flow through the system. DCN topologies are also categorized based on their switching techniques.

Electrical switching based topologies
The broad classification of network topologies based on electrical switching are of two kinds' switch-driven topologies and server driven topologies.
(i) Switch Driven Topologies In switch-driven DCs, switches assume the essential liability in system development and information transmission. Systems in traditional DCs are regularly developed dependent on a tree-based progressive topology with a few levels as per the system scale. A two level DC structural design comprises of two levels of switches known as edge and core switches which can hold millions of servers. But for huge scale DCs the three level structural design might be increasingly fitting, where switches are organized in three stages: edge, aggregate and core. Fat-Tree (Al-Fares et al. 2008), VL2 (Greenberg et al. 2009b), Portland (Mysore et al. 2009) are some examples in this category.
Fat Tree In most intra DCNs, this switch centric topology is used which offers full bisection bandwidth by interconnecting indistinguishable Ethernet switches. It is a unique example of a Clos topology which interconnects indistinguishable switches. Fat-tree is a high transmission capacity low latency topology. A 4-ary Fat tree is illustrated in Fig. 1, which consists of some switches arranged in three specific layers. Usually in a p-ary tree, (p/2) 2 servers with two layers of p/2 p port switches are contained in each pod. In the shown topology p/2 servers along with p/2 aggregate switches are connected to each edge switch. Then the flow of connection is carried forth next to the aggregate switch layer which is connected further to p/2 core switches and p/2 edge. Then there are p pods to which (p/2) 2 number of core switches are connected respectively.
The benefit of Fat tree is that all switches are similar and all switches can use inexpensive quality goods. Additionally there are several equivalent cost paths between any two hosts, so in principle maximum bisection bandwidth can be achieved. Fat tree's high cabling complexity is a downside for the network.
(ii) Server-driven topologies In switch-driven topologies, servers are just endpoints in the system. In any case, servers could assume a progressively significant job in intra DCN for the quick development of server equipment. In such networks servers perform both computing and packet switching. Using specialized servers, BCube (Guo et al. 2009), DCell (Guo, et al. 2008), and DPillar (Liao et al. 2010) provide solutions for accommodating hundreds of thousands of servers. Figure 2 depicts the concept of server-centric networking as in DCell.
DCell It is based on normal hierarchical server-centric topology through a recursive production. It interfaces servers (inside the equivalent rack) to a neighbourhood D cell that has a dreadful part higher network limit as contrasted and the tree-based topologies (Guo et al. 2008). D portable does now not make any bottleneck due to the appropriation of the traffic all through all connections. This structure utilizes servers outfitted with more than one system ports and littler switches, to helpful asset the improvement of its recursively portrayed engineering. On this system topology a server is joined to various others through smaller switches. Those hyperlinks are assumed to be bi-directional. DCell and similar proposals suffer primarily from the problem of packet Fig. 1 Basic Structure of Fat tree switching required to be performed by servers, a task that is not supported by generalpurpose servers.

Optical switching based topologies
The optical networking technology is well suited to meet the ever increasing bandwidth demand in data centers with a solution to network oversubscription and higher bit rate challenge. Optical network elements support on demand connectivity and capacity where required in the network, thus permitting the construction of thin but flexible interconnects for large server pools. Optical links can support higher bit rates, over longer distances using less power than copper cables (Calabretta et al. , 2016. Moreover optical switches run cooler than electrical ones, resulting in lower heat dissipation and cheaper cooling cost. C-Through and Helios provide a promising direction to exploit the optical networking technology for building DCNs. But OSA achieves high flexibility by leveraging and extending the prior devised techniques. OSA (Optical Switching Architecture) OSA, a novel Optical Switching Architecture for DCNs, leveraging runtime reconfigurable optical devices. OSA dynamically changes its topology and link capacities, thereby achieving unprecedented flexibility to adapt to dynamic traffic patterns. It investigates the achievability of a totally optical based system among ToR switches. It includes optical transceivers within ToR switch with different fibers for send and receive data packets (Chen et al. 2012).The multiplexers (Mux) to multiplex several fibers optical signals to one fiber's output and the 1 × 4 Wavelength Selective Switch (WSS) forward the signal to 4 DWDM channels or wavelengths. The circulators are used to achieve bi-directional transmission over a single fiber. The MEMS used over here is a 16 × 16 bipartite optical switch which grants associations from any informative port to any of the yield ports. The signals of different wavelengths are combined into one fiber by coupling and the de-multiplexers (De-Mux) just does the reverse function of a Mux, thus results multiple wavelength to different fibers from a single optical signal. In view of the assessed traffic request, the WSS and MEMS switches are reconfigured (Fig. 3).
OSA, in its existing form, has constraints, such as scaling of OSA to a larger DC with millions of servers from a container size is a big challenge, which in turn needs enormous  (Chen et al. 2012).The first obstacle is the port density of MEMS. While the MEMS 1000-port is hypothetically possible, there are 320 ports in the largest MEMS starting today. One characteristic approach to expand the port thickness is by means of interconnecting numerous little MEMS switches. Notwithstanding, this represents extra prerequisite for quick organized circuit switching. Furthermore, bigger system size requires more control and traffic management. Additional, the increase in end to end delay is another considerable issue.

Electrical/optical switching based topologies
The electrical transmission technology based data centers networks rely on electronic switching elements and point-to-point (ptp) interconnects. The electronic switching is realized by commodity switches that are interconnected using either electronic or optical ptp interconnects. Due to the high cross talk and distance dependent attenuation very high data rates over electrical interconnects can be hardly achieved. As a consequence, a large number of copper cables are required to interconnect a high-capacity data center, thereby leading to low scalability and high power consumption. Optical transmission technologies are generally able to provide higher data rates over longer transmission distances than electrical transmission systems, leading to increased scalability and reduced power consumption. Hence, recent high-capacity data centers are increasingly relying on optical ptp interconnection links. However, the energy efficiency of ptp optical interconnects is limited by the power hungry electrical to-optical (E/O) and optical-to-electrical (O/E) conversion required at each node along the network since the switching is performed using electronic packet switching. The continual increase in the cost of optical switching devices is also an issue in designing data centers offering high bandwidth (Aleksic et al. 2012). The  (Imran et al. 2015).
Helios A Hybrid Electrical/Optical Switch: the topology of Helios is framed as a multilayered tree structure with pod and core switches. The core switches avail a flexibility and benefit effectively by combining the two complementary techniques of switching i.e. they can be either electrical or optical switches. The inter pod communication is usually handled by circuit switching (Farrington et al. 2010) but in the congested portion of inter pod communication packet switching helps to convey all-to-all bandwidth. The mix switching results power consumption, complexity reduction, and increased performance for a given traffic.
A number of hosts indicated as H as shown in Fig. 4 are present in each pod is linked to the pod switch through copper links. The pod switch also contains a number of optical transceivers indicated as T are connected to the core switching array. One half of the uplinks of each pod switch before connecting to a single optical circuit switch, pass through a passive optical Multiplexer labelled as M and the other half of the uplinks are connected to packet switches. The hybrid DC switch architecture essentially incorporates the advantages of both technologies and used as a fully equipped packet-switched network with same measures of performance but at low cost and complexity and less power consumption. This determines the traffic subset best suited for circuit switching and dynamically reconfigures the topology of the network at runtime based on changing patterns. It does not require any end host modification, rather it demands switch software modification.
This topology includes dynamically configured electrical and optical switches. The flow of traffic either to electrical or optical network is decided by the Helios. There is about 266 ms time required to change the traffic path in Helios, in which 12 ms is used for optical switching (Farrington et al. 2010). Thus it leads to a drawback of getting higher value of latency.
The architectures of existing data centers suffer from some disadvantages such as end to end delay, bandwidth, energy consumption and quick failover . Large organizations with voluminous traffic are required to interconnect their own data centers, Fig. 4 Basic Structure of Helios topology which are discretely stationed in remote locations, to maintain system efficiency (Benson et al. 2010).

Proposed hybrid data center network architecture
It's challenging to get an efficient design for DCs, which should be fault tolerant, more scalable and should offer less delay. In cloud data centers where resource abstraction and virtualization is a key requirement, limited connectivity prohibits flexible virtual machine migration across the data center and severely degrades the network performance. Because of the quick development of system traffic and the consistent increment in the handling intensity of multicore servers, data centers should empower more and more number of servers with more number of microprocessors per server. Followings are some of key issues which prevents any efficient DCs to perform with full capacity.
• Delay: increased network delay can lead to performance degradation for delay-sensitive applications. Long queuing delay in switches is the key culprit of high latency, induced by the traffic in data centers. • Server-to-server connectivity: in a specific topology the ratio of attainable bandwidth in worst case to the net bisection bandwidth between the end hosts is termed as oversubscription ratio. Over-subscription is a way of raising the total design cost. The oversubscription ratio quickly rises, going up through the layers of switches and routers. • Scalability: the exponential growth in traffic within data centers is a challenging task to control by switches and Ethernet links based architectures. The data centers furnished with large number of servers finds difficulty in supporting the traffic growth through its hierarchical design. • Energy efficiency: Data centers with electronic links and switches leads to consume major chunk of available power, so consequently in future data centers energy efficient interconnect should be thought of for saving significant energy in the data centers.
Keeping in view of the above issues, a hybrid architecture has been proposed in this paper with an objective of providing high scalability and low latency. The proposed architecture is the hybridization of Electrical system (Fat tree) at the base layer (Layer 1) with Optical switching technique and system (ShuffleNet) in layers on the top of it. The use of WDM technology proposed in this topology can appreciably exploits the optical switching based DCN with less power consumption and low end-to-end latency in this network.

The base layer: electrical switching based fat trees
Existing DC architecture largely depends on Top-of-Rack (ToR) switch as its base layer. ToR approach refers to the physical placement of network access switch in the top of a server rack. Servers are directly linked to the access switch in this method. Each server rack usually has one or two access switches. Then all the access switches are connected with the aggregation switch located in the rack. Only a small amount of cables are needed to run from server rack to aggregation rack. As for ToR, the cost of cables are reduced since all server connections are terminated to its own rack and less cables are installed between the server and network racks. Cable management is also easier with less cables involved. Technicians can also add or remove cables in a simpler way.
Conversely, capital and maintenance costs might be higher. The distributed architecture of a ToR design requires the need for more physical switches. There also is the potential that several ToR switches may end up being underutilized. This can result in unnecessary power usage and cooling increases without a direct benefit to performance. Finally, if the ToR architecture calls for a single in-rack switch to be deployed per rack, if that switch fails, an entire rack will be taken offline. For ToR, although the cables are reduced, the number of racks is still increased. The management of switches may be a little tricky. In addition, ToR approach takes up more rack space for the installation of switches.
Moreover, flexibility and enhancement in number of servers cannot be made possible by the use of ToR switches. To provide flexible scalability in the network, the use of Fat trees at the base layer has been proposed in this architecture.
The use of Fat tree at the base layer provides two fold advantages to the design: (i) All the commodity switches are similar in nature and properties and inexpensive as well, (ii) Existence of several equivalent cost paths between any two hosts provide maximum possible equal bisection bandwidth.
In a p-ary tree, (p/2) 2 servers with two layers of p/2 p port switches are contained in each pod and on total p 3 /4 number of servers are accommodated by the topology. In the suggested architecture a number of 8-ary Fat trees are considered where each individual tree can accommodate 128 servers and the structure of an 8-ary Fat tree is depicted in the following Fig. 5.

The middle layer: optical switching based ShuffleNets
The existing hybrid architecture is incapable for many cloud operation because its failure to cater the need for a sizable servers with an elephant traffic. Generally on the top of the base server layer, optical devices are employed for high data rate and bandwidth prospective. But these benefits are neutralized because of cost, non-availability of switches for randomly increased server in base layer, poor fault tolerance etc. Hence a trade-off is the need of the hours. As a result, the present architecture in this paper proposed a ShuffleNet based layers in place of optical devices based layer on the top of the base layer (server).
As a way to access the enormous bandwidth capacity of optical fibre for multi-user packet communications, ShuffleNet multihop lightwave networks have been suggested. The ShuffleNet (Hluchyi and Karol 1991) is built on a generalization of the impeccable shuffle connection pattern (Stone 1971;Patel 1981), which denotes to a multihop lightwave network. It is of interest because it provides packet routing paths similar to those represented by an ideal spanning tree, allowing efficient use of the channels of communication under uniform loads of traffic. The Network Interface Units (NIUs) in ShuffleNet are physically linked by a fiber bundle that passes through every NIU, with each NIU receiving and sending packets on an allocated fiber subset. A NIU serves as the interface between one or more user nodes and the means of network communication.
ShuffleNet (Sivarqan and Ramaswami 1991) is a well-known multi-hop virtual topology uses Wavelength Division Multiplexing (WDM) with intensity modulation as underlying physical topology. A basic ShuffleNet is designated as (s, t) ShuffleNet consisting of (ts t ) number of nodes. They are arranged as t number of columns and s t number of nodes in each column and tth column is wrapped around to the first in a cylindrical way (Acampora and Karol 1989). This architecture can overcome both wavelength-agility and pre-transmission coordination problems. There is a total of ts t+1 arcs in a ShuffleNet connectivity graph: to each user, s outgoing and incoming arcs are there. If a WDM channel is associated with each arc, then there will be total ts t+1 channels in the network, with s transmitters and receivers respectively for each user.
In a ShuffleNet connectivity graph groups of s users in each column transmit on a common channel, with a separate group of s users in the next column receiving on each channel. Thus there are s t−1 channels per column of users and t s t−1 channels altogether in the network. For i = 0, 1, 2, … … , s t−1 − 1 , users i, i + s t−1 , i + 2s t−1 , … … and i + (s − 1)s t−1 in a column transmit on a common channel that is received by j, j + 1, j + 2, … … .. and j + s − 1 in the next column, where j = (i(mods t−1 ))s . Such a ShuffleNet connectivity graph for 18-user (s = 3, t = 2) is illustrated in Fig. 6. In addition to the 1st layer of ShuffleNets which was connected directly with the Fat trees, a 2nd layer of ShuffleNets are also introduced in the proposed architecture. The upper layer ShuffleNets are connected to all the lower layer ShuffleNets like core switches in traditional electronic DCN architecture. Otherwise if one server from Shuf-fleNet 1 of layer 1 wants to connect to a server of ShuffleNet N of layer 1 then they have to be connected through the MEMS switch. Then in this situation the reconfiguration delay of MEMS switch will also be summed up with the end to end delay of the network and thus the overall communication delay for the given architecture will be automatically increased with respect to the variation in type of traffic.
Due to the emerging demand, now servers requires low delay and high bandwidth communication. Optical connectivity consumes less power at the same bandwidth provided by it is larger than electrical links. However, the optical switches, typically using micro-electro-mechanical switches (MEMS) (Dobbelaere et al. 2002), suffer from high delay (~ 10 ms) at the time of switch reconfiguration and hence cannot handle bursty traffic efficiently. Thus the proposed architecture is designed to bypass the traffic in such a way that end to end delay will not be much suffered by MEMS delay and better load balancing is achieved (Ghorbani et al. 2017;Yan et al. 2018).
Thus again the architecture depicts a 3rd layer of ShuffleNets, which will decide whether the traffic flow will be forwarded to MEMS (Optical Switch) or to the other ShuffleNet depending on the strength of traffic. If the traffic is an elephant traffic then we have to forward it to MEMS and through MEMS only it will be further connected to another ShuffleNet to ToR and this increase in delay that is offered by MEMS switch can't be avoided. But, if the traffic is a mouse traffic then it will be advised not to direct the flow to MEMS rather than directed through another ShuffleNet such that the extra increase of delay can be avoided. Within the ShuffleNet it is better to have, so that the end to end delay will be reduced, so for this purpose the 3rd layer of ShuffleNet is highly required. Thus the final layout of the proposed architecture can be framed as depicted in Fig. 7.   Fig. 7 The layout of proposed hybrid architecture In this architecture we restricted our study in the ShuffleNet based optical domain. Figure 8 shows the hierarchical ShuffleNet structure for the proposed model. Here there are three layers of ShuffleNets designated as ShuffleNet 1 (SNL1), ShuffleNet 2 (SNL2) and ShuffleNet 3 (SNL3). The first and second layer of ShuffleNets are controlled by the layer three ShuffleNet, so it can be treated as a master ShuffleNet. When the data is transferred from one ToR to another between two different ShuffleNet, packets are transferred through the master ShuffleNet, which consequently reduces the network delay. An optical switch is also connected in parallel with the master ShuffleNet to reduce the load in master ShuffleNet. If the packet size is too large then it follows the optical switch.

The upper optical switch layer
In a MEMS optical switch, a micro-mirror is used to reflect a light beam. The direction in which the light beam is reflected can be changed by rotating the mirror to different angles, allowing the input light to be connected to any output port. This type of optical switch has been realized for the first time through the fusion of various techniques such as micro-machining techniques for fabricating the mirror, optical design techniques for achieving low-loss optical connections, and control techniques for positioning the mirror accurately. It can switch optical signals without converting them into electrical signals. It allows compact low-loss switches to be formed on any scale. The switching can be performed in 10-30 ms. Since this device can switch large numbers of optical signals simultaneously, it can be used as a trunk switch for handling large amounts of traffic, and as a switch in large urban communication networks.

The Final Structure of the Proposed Hybrid Architecture
The proposed architecture is designed on the basis of accumulating higher number of servers under the net with lower latency. In layer 1 of ShuffleNet, four 8-ary Fat trees are connected through 16 core switches. So under each ShuffleNet of layer 1 minimum 4 × 128 servers will be there. For small dimension of Fat tree, the delay will be less but consequently number of Fat trees under the ShuffleNet will be increased resulting more number of hops and as a result ShuffleNet delay will be increased. Thus a trade-off must be taken in the selection of size of Fat tree to reduce the end to end delay in the network. The configuration of layer 1 ShuffleNet is set based on the structure of the fat tree interconnected with it. When 8-ary Fat trees will be there, then they need minimum of 64 + 1 + 1 = 66 (4 × 16 = 64 ports with respect to the requirement of fat tree+ 2 ports for O-E-O conversion with respect to the connection to next level of ShuffleNet and to the higher level of optical MEMS switch) ports in the ShuffleNet. Thus according to the configuration there is logically availability of 81 (s = 3, t = 3) ports in ShuffleNet but at the same time if the physical availability of NIUs will be thought of then 128 port switches are considered.
Similarly in the 2nd layer of ShuffleNet in each ShuffleNet logically minimum 24 (s = 2, t = 3) port switches are required as to connect with 16 core switches of a particular Fat tree, but physically available switch port of ShuffleNet is 32. Each and every ShuffleNet in the 2nd layer is connected to the first layer ShuffleNets with 80 ports as therefrom one port is directly connected to the upper layer. The last upper level of ShuffleNet should have minimum 24 ports to accommodate the 24 port ShuffleNets in layer 2.
The topmost layer of the architecture consists of a 24 × 24 MEMS optical switch. Higher dimension MEMS switch will offer more delay in configuration and power loss. In the proposed architecture huge traffic can be accompanied with a lower dimension switch.
With respect to the proposed architecture if a 4-ary (4 × 16) fat tree will be considered then a (2, 2) ShuffleNet is sufficient enough to accommodate two 4-ary Fat trees, because a 4-ary Fat tree consists of 4 core switches with 4 available ports for communication and a (2, 2) ShuffleNet has 8 available ports. So in the other way it can also be stated that a single (2, 2) ShuffleNet can accommodate 16 servers. So generalizing the above example the total number of servers accommodated by the proposed architecture can be stated as follows….
If in a p-ary Fat tree total number of servers = p 3 /4, then under one ShuffleNet there will be N × p 3 4 servers. Thus for M such ShuffleNets the total number of servers will be Then consequently the total number of servers under MEMS (R x R) will be All the logical or physical configurations of the ShuffleNets are chosen based on their throughput in consideration with the database shown in Table 1 (Acampora and Karol 1989).
Therefore the total number of servers encompassed with respect to the given configuration of the proposed architecture will be ( Fig. 9)

End-to-end delay computation
The proposed architecture of the data center network has been made as three layer system, the first (base layer) of which consist of Fat trees. The subsequent (middle) layers, 2nd and 3rd tiers, are of Shuffle-net and the top layer, the 3rd layer, comprises up of MEMS switch. Thus the total end to end delay for the proposed architecture is the sum of end-to-end delay in each tier in the hierarchy. The complexity involved in end-to-end delay computation in Fat trees based layer is addressed by the help of queueing theory. In the following we have deduced the delay computation for each layer.

Delay in base layer: end-to-end delay in fat-tree topology
Fat-tree can be modelled by forming an open tandem queuing model in which each node has a FIFO buffer of infinite size and packets pass through a series of rely nodes towards a sink node. In an open queuing network, packets enter and depart from the network. The arrival times of packets at the receiving node in a tandem queue are interrelated with their previous node departure times. Therefore, an M/M/n model based on Jackson Network is appropriate to analyse the behaviour of each communication link. The Fat tree topology under consideration with aggregate traffic flow from the external and relay flow is depicted in Fig. 10. It shows a partial structure of the Fat tree topology depicted in Fig. 5. Both external and relay flows are aggregated with cumulative rate entering the node j and let r ij is the probability of routing a packet between node i and j . The probability r ij = 1 is obtained when a packet reach to node j leaving node i . In a Jackson network denoted as R P n×n is n × n probability matrix which describes the routing of the packets within the Jackson Network (Jackson 1957). The following assumptions are observed in the Jackson network consisting of n self-independent M/M/n queuing system.
(1) The system only accepts the arrival of packets of one class.
(2) At node j packets are arriving with a rate j ≥ 0 obeying Poisson distribution.
(3) The service time at jth queue is exponentially distributed with mean of average packet duration j . (4) The specified packet may proceed to node j , upon receiving its service at node I with a priori probability of r ij or may leave the node j with a probability of (1 − r ij ). (5) From any node, there exist at least one route to the final destination node, such that r ij = 1 Let λ = [λ 1 , λ 2 , …, λ n ] is the average arrival rate of imparted packets. γ = [γ 1 , γ 2 , …, γ n ] is the average arrival rate of the other external packets. r ij = a priori probability of the routing packets from node i to node j and Assuming there is no blocking and hence each node has infinite queue capacity, the total arrival rate to the node j at steady state of the network is Representing in vector form, for all the nodes n The aggregate arrival rate vector is solved by, Let us assume that the external traffic is mutually independent and Poisson distributed with rate j . So the service times of the same packet in any other nodes are independent of the arrival rates. Each node can be treated as an individual queuing system after the decomposition of the network if the resultant rate at each node is known. Thus it may be thought of like that the average queuing delay is equivalent to the corresponding M/M/1 queue. So the aggregate packet arrival rate is Let us define j = j j which indicates that the transmitting buffer is not empty at node j for fraction of the time which suggests node j has a packet to transmit. According to Jackson's Theorem (1957) the joint steady state distribution for the number of packets at each node is given by: where L n denotes the length of queue at node n and n n denotes number of nodes. Applying Little's formula, which states that, for systems that reach steady state, the average number of packets in a system is equal to the product of the average arrival rate and the average time spent in the system: For downlink delay, the direction of the incoming traffic goes from clients to servers as shown in Fig. 11 with an illustration by considering a 4 × 16 Fat tree. So traffic in this direction does not face any contraction point as the number of output-ports at each switch are either equal to or greater than input-ports. So the topology has a very low delay with downlink traffic as compared to the uplink traffic where traffic travels from servers to clients.
The delay for the above structure in downlink direction is determined for a number of utilization rate as depicted in Table 2.
Similarly the traffic traveling from servers to client in an uplink direction as shown in Fig. 12 is another significant traffic. Traffic would be at the core level of this model during a concentration point, leading to a rise in delay as observed from Table 3.
At each node the average arrival rate is calculated for specific downlink traffic and thus it leads for the calculation of the probabilistic end-to-end delay at each node and for an end-to end connection. From the above table metrics it is observed that the average delay for a full end to end communication in a DCN with Fat tree is at maximum value of 0.0548 ms. Thus this approach of network topology leads to the design of an efficient DCN with respect to delay sensitive applications.

Delay in middle layer: delay in ShuffleNet
The multiple WDM channels with a fixed routing algorithm are efficiently used by the ShuffleNet under uniform traffic loads, which is a significant feature of ShuffleNet as a Thus, between any two randomly selected users, the expected number of hops is given by  For a (s, t) ShuffleNet delay will be calculated as the product of expected number of hops and the average packet duration. If the real value of packet size is 10,000 bits and bit rate be 10 GBPS, with bit duration of 0.1 nsec, then for 10,000 bits the delay will be 10,000 × 10 −10 sec, which is equal to the average packet duration. For example in a Shuf-fleNet with 18 users, s = 3 and t = 2, the expected number of hops using Eq. (6) is found to be 2.176. Thus the delay offered in this net will be

Delay in upper layer: delay in MEMS
The MEMS based switches have high tuning time, in the range of few milliseconds. So when delay in the network matters, we need to do some necessary arrangements to avoid the transmission of traffic though such switches. MEMS is the most popular OSM (Optical Switching Matrix) technology and achieves reconfigurable at 10 ms (Truex et al. 2003) by adjusting the micro mirrors mechanically.

Total delay for the proposed Architecture
Total Delay for the proposed Architecture for a mouse traffic: The total delay for a mouse traffic is the sum of delays in each tiers with bypassing MEMS through the 3rd layer of ShuffleNet Total Delay for the proposed Architecture for an elephant traffic: The total delay for a mouse traffic is the sum of delays in each tiers

Conclusion
The proposed DCN hybrid architecture provides significant reduction in end-to-end delay while routing mouse traffic to elephant traffic as compared to OSA system. The present architecture makes use of three layers of ShuffleNet based topology in the middle layer and hence capable of bypassing higher dimensional MEMS switch which is a major cause of delaying in the routing. One ShuffleNet takes care of 4 numbers of 8-ary Fat trees at the base layer and as such we have employed 81 numbers of such ShuffleNets to cater the need for 995,328 numbers of servers with 24 × 24 MEMS switch. With such a huge number of scalability, the end-to-end delay for the worst case scenario is computed as 10.01 ms, whereas in OSA it is 23 ms. In OSA, the end to end delay is based on two critical devices used over there i.e. Optical Switching Matrix (OSM) and Wavelength Selective Switch (WSS). The switching delay of OSM in OSA-2560 is 9msec and similarly the reconfiguration time of the WSS is around 14msec because of wavelength channel switching among two output ports which leads to a high value of delay for the network. Thus the total delay offered by this model for a given traffic is 23 ms. It is pertinent to presume that use of substantial number of optical devices require relatively less power as compared to its electrical counterpart. The net power consumption for the proposed architecture based on commercially available devices can be calculated to provide relief to the host from the burden of the cost incurred due to power tariff.