Description of an Application of Queueing Network Modelling

The model presented in this chapter represents a physical network system of a number of nodes through which objects (i.e. USVs) flow, as shown in Figure 38. This model representation is seen to be a generic structure demonstrating the USV-mothership interfaces. More or less detailed models could be generated from such a generic network structure, depending on the nature of the problem and the level of detail necessary to capture the design aspects under interest, such as those related to LAR operations. According to this model, the tasks of a fleet of USVs supported by a mothership are represented using the following nodes:-

 The deployment of each USV starts with preparations that include appropriate quick pre-mission checks (pre-mission checks node);

 The vehicles stowed in the mission bay(s) are moved (movement node) towards the launching facilities, by using internal mission bay handling systems (e.g. overhead crane paths, trolleys);

 The vehicles are launched (launch node) into the water from the mothership;

 Once launched, they head towards the mission theatre (mission theatre node) to perform certain tasks according to the appropriate CONOPs scenario. While on-station the vehicles are remotely controled and operated through C3 systems and sensors;

 In case of a detected malfunction (malfunction at sea node) the implicated vehicle may abort the mission and head back to the mothership (or other support vessel) to be recovered on-board for repairs and re-launcing thereafter.

A more efficient option would be "repair by replacement", which means spare stowed vehicles are launched to replace the malfuntioning ones;

 Given the power and munition capacity of a USV is rather limited, it may be necessary for every vehicle to be able to refuel and rearm close to or even at the mission theatre i.e. on-station (refuel and ordnance node);

 When the operations at a mission theatre are completed, all vehicles return to the mothership to be recovered on-board (recovery node);

 Once the vehicles are recovered on-board, they are maintained (maintenance node), if necessary, and get prepared for the next potential mission (refuelling and rearming nodes);

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 Finally, the vehicles are stowed (stowage node) in the mission bay(s) with the assistance of internal handling systems and the cycle can then be repeated.

It is noteworthy that the models investigated in this research:-

 Represent the flow of UXVs through a queueing network system consisting of a number of nodes/activities, as discussed above, and not a sequence of discrete processes (consideration of issues is given at page 285 in Appendix 6);

 Are deterministic, since the routing ratios are defined by the user;

 When disabled vehicles return to the mothership, they are assumed to not interfere with the flow process.

147 Figure 38: Queueing network model

148 This model involves two different types of USVs, termed vehicles of Type "A" and Type "B".

Such vehicle types are hypothetical, with Type "A" having similar size to a RHIB (i.e. 11 m) and Type "B" being smaller non-disposable USV (i.e. ~ 3 m), respectively. It is likely that multiple types of USVs would be operated from a mothership to meet fleet adaptibility criteria according to the various mission requirements. Using different USV types also demonstrates that the QT tool is capable of modelling complex UXV systems consisting of different types of uninhabited assets. It is sensible to model different UXV types, as they are likely to require distinct service facilities. The model describes the deployment of Types "A" and "B" vehicles in the theatre of operations, in order to perform allocated tasks according to CONOPs scenarios (i.e. abstracted scenarios, since CONOP studies were not undertaken in this research), denoted as "Mission 1" and "2". In this study, 60 USVs are deployed from a single mothership, 20 of them are USVs Type "A" and 40 are USVs Type "B". The vehicles flow through the nodes in the network system, shown in Figure 38, where they perform certain tasks (i.e. activities) following a path (i.e. route) indicated by the connectivity lines that form the particular network structure. The number of vehicles departing from each node in the network system and heading to the next node, according to the indicated path/route, is defined by the routing ratios, which form a K x K matrix (i.e. network of K nodes). The routing ratios show the number of vehicles heading to node j over the total number of vehicles present at node i. Hence, for the vehicles departing from node i towards node j, the routing ratio is defined as:

P

=

Any node represents a task in the network system, where the inputted data for this model are given in Table 10. Such data for each node in the network system include, the node name, the node number used in the analysis of the system, the type of the servers per node, the number of servers per node and the processing duration (i.e. service). Table 10, also shows which nodes of the network system refer to either on-board or off-board tasks and highlights whether a node is likely to have an impact on the mothership configuration or/and the operated USVs. The on-board nodes represent facilities and any necessary relevant resources that must be integrated into the mothership configuration, thus directly affecting the overall mothership design.

However, the off-board activities do not directly impact the design of a mothership. While the nodes modelling the recovery operations are on-board nodes, their implications on the design

149 of a mothership only involve the equivalent service area demands (i.e. LARS installation and integration). This is because any recovery queueing activities would take place at sea and not on-board the mothership (i.e. nil queueing area demands). Finally, the facility levels per node reflect the maximum number of vehicles that can be simultaneously served by the servers of each node.

150 Network Structure Nodes

Node Name Node

Number Node Service Area Node Space Requirement Ship/Vehicle

Impact

151 Table 10: Description of nodes in the queueing network of Figure 38

Node Name Node

Number Node Service Area Node Space

Requirement

* The values of the facility levels and processing times provided in this table are indicative, in order to demonstrate the tool’s capabilities and do not necessarily represent actual model derived data or realistic values

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4.3 Translation of Queueing Network Modelling into Mission Bay