A multi-layer agent simulation method and system for vehicle-road collaborative computing

Abstract

The application relates to a multi-layer intelligent agent simulation method and system for vehicle-road coordination computing, the method comprising the following steps: S1, a basic data input module reads information data of a satellite map, road ontology facilities, road area intelligent equipment and vehicles; S2, a road scene construction module constructs a road scene; S3, a traffic operation control module constructs a traffic control model and continuously updates a control scheme; S4, a vehicle-road coordination computing module performs computing task distribution, processing and feedback; and S5, a result visualization module outputs traffic and communication evaluation indexes under various traffic scenes. The method constructs intelligent road simulation scenes under different road basic environments, traffic flow and road area-vehicle external information interaction strategies, optimizes road area intelligent equipment layout, traffic control and vehicle-road coordination computing strategies, realizes full-process simulation of computing task distribution, processing and feedback between road area communication computing units and intelligent vehicles, and outputs traffic and communication evaluation indexes under various scenes.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation technology, and in particular to a multi-layer intelligent agent simulation method and system for vehicle-road cooperative computing. Background Technology

[0002] With the development of new technologies such as intelligent driving, vehicle-to-everything (V2X) communication, each vehicle needs to have a comprehensive and accurate grasp of information about the vehicle, road, and environment in real time, resulting in a significant increase in various computing tasks. Fully utilizing the vehicle's idle computing power and roadside communication computing units to collaboratively perform computing tasks can effectively improve the overall computing capabilities of the system.

[0003] Existing research primarily focuses on the mobile communication layer, emphasizing the optimization of computational task allocation algorithms between vehicles and roads. Based on roadside units (RSUs) equipped with Mobile Edge Computing (MEC) servers, Guo et al. demonstrated that a deep reinforcement learning-based intelligent task allocation algorithm can significantly reduce the computational burden on vehicles. Shahidinejad et al. further improved the allocation effect by introducing a context-aware mechanism. Liu et al. further considered the dependency constraints between different computational tasks and proved that their proposed optimization framework has lower system computational latency compared to existing allocation methods.

[0004] With the continuous development of vehicle-to-everything (V2X) technology and its organic integration with vehicle-to-everything (MEC), vehicular edge computing (VEC), a new paradigm for improving vehicle computing performance, has developed rapidly. As VEC nodes, the constantly moving vehicles cause rapid changes in the V2X topology. Compared to MEC, VEC presents new requirements for target computing node selection, multi-hop transmission task allocation, and opportunistic computing network construction. For example, regarding the node selection problem, Hamdi et al. constructed a service level protocol to ensure the selection of the optimal computing node, thereby achieving efficient utilization of idle vehicle computing resources. Regarding the multi-hop transmission problem, Liu et al., based on single-hop transmission task allocation, fully utilized the computing resources of multi-hop vehicles to significantly reduce system latency. Regarding the opportunistic computing problem, Rahman et al. considered real-time state information such as vehicle speed, direction, and position, and designed a context-aware opportunistic network construction scheme, effectively reducing task waiting time and improving the success rate of collaborative computing.

[0005] In summary, current research mostly focuses on optimizing the allocation of computational tasks to improve computing power utilization efficiency, thereby reducing system computational latency. Less research addresses vehicle-road cooperative computing, designing simulation systems to verify the latency variations of vehicle-road cooperative computing under different scenarios. This invention addresses the elements involved in vehicle-road cooperative systems, such as intelligent road infrastructure, vehicle operation management, and vehicle-road communication computing, and designs a multi-layered intelligent agent simulation model comprising an infrastructure layer, a traffic operation layer, and a cooperative computing layer. Summary of the Invention

[0006] The purpose of this invention is to propose a multi-layer intelligent agent simulation method and system for vehicle-road cooperative computing, and to verify the time delay variation law of vehicle-road cooperative computing under different scenarios.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A multi-layer intelligent agent simulation method for vehicle-road cooperative computing, comprising:

[0009] The S1 basic data input module reads information data from satellite maps, road infrastructure, roadside intelligent devices, and vehicles;

[0010] The S2 road scene construction module constructs road scenes;

[0011] The S3 traffic operation management module constructs a traffic management model and continuously updates the management plan;

[0012] The S4 vehicle-road cooperative computing module distributes, processes, and provides feedback on computing tasks.

[0013] The S5 results visualization module outputs traffic and communication evaluation indicators for various traffic scenarios.

[0014] A further improvement of the present invention is that, in step S1, the steps performed by the basic data input module include: reading information data from satellite maps, road infrastructure, roadside intelligent devices, and vehicles; wherein:

[0015] The basic elements of road infrastructure include materials, alignment, and signage / markings;

[0016] Intelligent roadside equipment includes sensing, computing, communication, and control units; the sensing unit collects vehicle location and operating status information and transmits it to the traffic operation control module through the communication module.

[0017] The vehicle information includes computing power parameters, communication range, speed, driving direction, current location, and vehicle type.

[0018] A further improvement of the present invention is that the process of the road scene construction module constructing the road scene in step S2 includes:

[0019] (1) Extract the horizontal linear features of the road based on the satellite map and perform coordinate transformation to generate a linear road network topology, i.e., the basic layer of the road infrastructure.

[0020] (2) Construct a road domain communication computing unit optimization deployment model, update the model parameters to meet different smart road service needs, and generate a device layer based on point elements;

[0021] (3) Import information on smart road facilities and equipment into the database;

[0022] (4) A geographic information map is constructed by combining a multi-layer road network and a database to create a road scene.

[0023] A further improvement of the present invention is that, in step S3, the traffic control model constructed by the traffic operation control module includes: signal control, variable speed limit, and tidal flow lanes; the process of generating the control scheme includes:

[0024] (1) Set the driving behavior parameters of the vehicle intelligence agent, specifically including the parameters of car following behavior and lane changing behavior. The initial speed, acceleration and other parameters of different vehicle intelligence agents follow a given distribution.

[0025] (2) Construct a traffic control model, including signal control, variable speed limit, and tidal flow lanes;

[0026] (3) Based on indicators such as vehicle travel delay and intersection queue length, update the control plan and its parameters.

[0027] A further improvement of the present invention is that, in step S4, the process of vehicle-road cooperative computing module distributing, processing, and providing feedback on computing tasks includes:

[0028] (1) The vehicle intelligent agent generates a certain size of computing task at a certain frequency and includes all vehicles and road communication computing units within its communication range into the candidate computing node set;

[0029] (2) Based on the given task allocation rules, select computing nodes from the candidate set and allocate computing tasks;

[0030] (3) After the selected node completes the task processing, it sends the result back to the original vehicle.

[0031] A further improvement of the present invention is that, in step S4, the vehicle-road cooperative computing module adopts a vehicle-road cooperative computing task allocation method based on the water injection method to select computing nodes from the candidate set and allocate computing tasks.

[0032] A further improvement of the present invention is that, in step S5, the content output by the result visualization output module includes:

[0033] (1) Output traffic evaluation indicators for various traffic scenarios, including vehicle travel delay, intersection queue length, and road service level;

[0034] (2) Output communication evaluation indicators for various traffic scenarios; In the S4 vehicle-road cooperative computing module, after the computing task is successfully assigned, it will go through four stages: sending the task to the target node, queuing the task before processing at the target node, computing and processing the task, and sending the computing result back to the original node. The system computing latency T latency The calculation formula is as follows:

[0035] T latency＝ T request +T queuing +T process +T response

[0036] Among them, T request For transmission delay, T queuing For the waiting delay, T process To handle latency, T response For the return transmission delay.

[0037] The present invention also provides a multi-layer intelligent agent simulation system for vehicle-road cooperative computing, comprising: a basic data input module, a road scene construction module, a traffic operation control module, a vehicle-road cooperative computing module, and a result visualization module; used to execute the above-mentioned multi-layer intelligent agent simulation method for vehicle-road cooperative computing.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] This invention provides a multi-layer intelligent agent simulation method and system for vehicle-road cooperative computing. It constructs intelligent road simulation scenarios under different road infrastructure environments, traffic flow, and external information interaction strategies such as road-vehicle interaction. It optimizes the deployment of intelligent road devices, traffic control, and vehicle-road cooperative computing strategies. It realizes the full-process simulation of the allocation, processing, and feedback of computing tasks between road-domain communication computing units and intelligent vehicles. It outputs traffic and communication evaluation indicators under various scenarios and can verify the latency variation law of vehicle-road cooperative computing under different scenarios. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0041] Figure 2 This is the multi-layer intelligent agent simulation model architecture of the present invention;

[0042] Figure 3 This is the simulation model flow of the multi-layer intelligent agent of the present invention;

[0043] Figure 4This is a schematic diagram of a road scene in a specific embodiment of the present invention;

[0044] Figure 5 This is a diagram showing the vehicle-road cooperative computation delay results in a specific embodiment of the present invention. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0046] like Figure 1 As shown, a multi-layer intelligent agent simulation method for vehicle-road cooperative computing includes:

[0047] S1 Basic Data Input Module: Reads data from satellite maps, road infrastructure, roadside intelligent devices, vehicles, etc. Road infrastructure includes basic elements such as materials, alignment, and markings. Roadside intelligent devices include sensing, computing, communication, and control units. Vehicle information includes computing power parameters, communication range, speed, etc.

[0048] The S2 road scene construction module extracts road planar linear elements from satellite maps and performs coordinate transformation to generate a linear road network topology, i.e., the basic layer of road infrastructure. Addressing different smart road service needs, it optimizes the deployment locations of road-area communication computing units, generating a device layer based on point elements. Subsequently, smart road infrastructure and device information are imported into a database to form a geographic information base map, thus constructing the road scene.

[0049] The S3 traffic operation management module constructs various traffic management models, including signal control, variable speed limits, and tidal flow lanes. Based on real-time perception of traffic operation status, it continuously updates management plans to improve road service levels, aiming to reduce vehicle travel delays and intersection queue lengths.

[0050] The S4 vehicle-road cooperative computing module encompasses the entire cooperative computing process, including task distribution, processing, and feedback. After a vehicle generates a computing task, it establishes communication with neighboring vehicles and roadside communication computing units within a certain range. Based on given rules, it selects the optimal node to form a transmission link and allocates the computing task. After the selected node completes the task processing, it feeds the calculation results back to the original vehicle.

[0051] S5 Results Visualization Module: This module outputs traffic and communication evaluation indicators for various traffic scenarios;

[0052] This specific embodiment uses AnyLogic as the simulation platform to illustrate the invention. Figure 2 This is the multi-layer intelligent agent simulation model architecture of the present invention. Figure 3This is the simulation model flow of the multi-layer intelligent agent of the present invention.

[0053] The specific process of step S1 is as follows:

[0054] Step 1.1: Read the satellite map and take the urban road segment with at-grade intersections as a typical specific example scenario. The length of each road segment in the direction of entrance is 200m, which includes one dedicated left-turn lane and one dedicated straight lane. The right-turn lane adopts channelization diversion measures.

[0055] Step 1.2: Read the road infrastructure, including basic elements such as materials, alignment, and markings;

[0056] Step 1.3: Read the roadside intelligent devices, including sensing, computing, communication, and control units. The sensing unit collects vehicle location and operating status information and transmits it to the traffic operation control module via the communication module.

[0057] Step 1.4: Read vehicle information, including computing power parameters, communication range, speed, driving direction, current location, vehicle type, etc.

[0058] The specific process of step S2 is as follows:

[0059] Step 2.1: Based on the satellite base map, extract the key nodes and distance reference information of the road alignment, and convert them with the map scale to obtain the Cartesian plane coordinates of each point in the simulation system, and draw the road alignment in the simulation system;

[0060] Step 2.2: In this specific embodiment, to minimize the impact of the road domain communication computing unit deployment scheme on the vehicle-road cooperative computing effect, only one set of road domain communication computing units is introduced. Simultaneously, to ensure that the distance attenuation of the road domain units for vehicles in all directions is the same, they are deployed in the center of the intersection. Furthermore, their coverage area is set to ensure that a communication link can be established with all vehicles in the simulation scenario. The road domain communication computing unit can fully cover the spatial range of this example;

[0061] Step 2.3: Based on the actual road plan information and pavement design, set parameters such as lane direction, number, connectivity, and pavement materials to complete the construction of the basic road infrastructure base map, and import smart road facility information (such as anti-skid pavement performance parameters) and equipment information (such as equipment performance and deployment location parameters) into the database;

[0062] Step 2.4: A geographic information map is constructed by combining a multi-layered road network with a database, creating a road scene, such as... Figure 4 As shown;

[0063] The specific process of step S3 is as follows:

[0064] Step 3.1: Set the driving behavior parameters of the vehicle agent. The target speed of the vehicle agent is 60 km / h, and the maximum acceleration is 1.8 m / s². 2 The maximum deceleration is 4.2 m / s². 2 ;

[0065] Step 3.2: Set the traffic flow input for the minimum and maximum traffic volume scenarios to 80 pcu / h and 800 pcu / h (i.e., saturation traffic volume), respectively, and increase them sequentially in increments of 80 pcu / h in each scenario. Other traffic flow parameters (such as the turning ratios of each approach lane) are all actual data obtained from the survey at this intersection.

[0066] Step 3.3: Design the intersection signal control scheme. This specific embodiment sets up four phases: north-south straight, north-south left turn, east-west straight, and east-west left turn. A timing control strategy is adopted, and parameters such as the signal control cycle and the green light duration of each phase are calculated according to Webster's timing method.

[0067] The specific process of step S4 is as follows:

[0068] Step 4.1: In this specific embodiment, the average computing power of the vehicle agents is set to 400 TOPS (trillion operations per second). Considering the differences in computing power among different vehicles in actual road traffic scenarios, different degrees of heterogeneity in vehicle computing power are introduced in the simulation scenario design. Specifically, the absolute value of the difference between the extreme value and the mean of vehicle computing power in the system is set to 0%, 25%, 50%, 75%, and 100% of the mean computing power (i.e., 400), respectively, and follows a triangular distribution. In addition, in the extreme scenario with a proportion of 100%, when a vehicle agent with zero computing power appears, its computing power is set to 0.1 TOPS to avoid situations where vehicles cannot handle computing tasks, thereby ensuring that all vehicles can complete the processing of computing tasks within a finite time.

[0069] Step 4.2: In this specific embodiment, the computation task generation interval and computation workload of the vehicle intelligent agent are set to follow a symmetrical triangular distribution. The computation task generation interval μ ~ Δ(50, 150), in milliseconds; the computation workload τ ~ Δ(20, 40), in trillions of operations.

[0070] Step 4.3: In this specific embodiment, the computing power of the road domain communication computing unit is set to 0 or 10 times the average computing power of intelligent vehicles. 0 10 1 10 2 With 10 3 The computing power of the road-domain computing communication unit is 0, 400 × 10 times. That is, the computing power of the road-domain computing communication unit is 0, 400 × 10 times respectively. 0 400×10 1 400×10 2With 400×10 3 TOPS. Among them, the scenario where the computing power of the road unit is 0 represents a pure vehicle-to-everything (V2X) environment without the support of intelligent roads.

[0071] Step 4.4: This specific embodiment designs a vehicle-road cooperative computing task allocation method based on the water injection method, according to the maximum computing power c of the vehicle or road domain communication computing unit node v. v Based on the total computational tasks already processed, the threshold for allocating computational tasks, i.e., the waterline WL, is found. On the basis of balancing system performance and resource consumption, the total computing capacity of the system is maximized. Its pseudocode is shown in Table 1.

[0072] As shown in Table 1: The inputs to the computational task allocation algorithm based on the water-filling method include: vehicle or road area communication computing unit node v s Calculate the task size τ; vehicle communication coverage radius r v The coverage radius r of the road area communication computing unit r The total computational tasks for the vehicle are f(t), the total computational tasks for other vehicles are g(t), and the total computational tasks for the road are h(t); its output is: the optimal computation node.

[0073] The computational task allocation algorithm based on the water-filling method includes (1) searching for the optimal water-filling line, (2) calculating the amount of tasks to be allocated, (3) selecting cooperative computing nodes, and (4) determining whether the task can be successfully sent and updating the amount of computational tasks. Wherein:

[0074] (1) During the search for the optimal water level, the water level WL is first initialized:

[0075] WL=min(f(t),g(t),h(t))+c v / 3

[0076] Define and update the reference value ρ of the water injection line t :

[0077] ρ t =(WL-f(t)) + +(WL-g(t)) + +(WL-h(t)) +

[0078] Continuously update the water level WL and reference value ρ t , until |c v -ρ t |>ε; where: the expression for updating the water injection line WL is:

[0079] WL = WL + (c v -ρ t ) / 3

[0080] Update reference value ρ t The expression is:

[0081] ρ t =(WL-f(t)) + +(WL-g(t)) + +(WL-h(t)) +

[0082] (2) The stage of calculating the amount of tasks to be assigned specifically includes:

[0083] Calculate the allocatable computational resources c below the water injection line. t Its expression is:

[0084] c t =WL-(f(t)+g(t)+h(t))

[0085] The calculation of the task allocation ratio λ for other nodes is expressed as follows:

[0086]

[0087] Calculate the computational workload w of other nodes k Its expression is:

[0088] w k =λ×τ

[0089] (3) The stage of selecting collaborative computing nodes specifically includes:

[0090] Define the candidate computation node set S, whose expression is:

[0091]

[0092] Based on the node's computing power c s Calculate the maximum completion time t of the task. max Its expression is:

[0093] t max =max{∑τ / c s :v s =S}

[0094] Initialize compute nodes For self-driving cars v v Initial score:

[0095]

[0096] In v s ∈S∧v s ≠v v In this case, the following steps are executed repeatedly:

[0097] Determine whether the calculation node is consistent with the direction of the vehicle's movement.

[0098] If they match, the score is calculated based on their relative speed. Its expression is:

[0099]

[0100] Otherwise, the score is calculated based on the relative speed. Its expression is:

[0101]

[0102] Scores are calculated based on task processing ability. Its expression is:

[0103]

[0104] Compare the scores of the current node Score of candidate node

[0105] If it is less than, then update the compute node and its score, expressed as:

[0106]

[0107] (4) The stage of determining whether the task can be successfully sent and updating the calculated task quantity specifically includes:

[0108] To determine whether a task has failed to send, the expression is random(0,1)<p;

[0109] If the transmission fails, update the computational task quantity f(t) of the autonomous vehicle, and calculate the node and score to update the autonomous vehicle; where: the expression for updating the computational task quantity f(t) of the autonomous vehicle is:

[0110] f(t)=f(t)+τ

[0111] The expression for calculating the node and updating the score back to the vehicle is:

[0112]

[0113] If the task is successfully sent, there are two possibilities:

[0114] (4.1) If the computing node is another intelligent vehicle Then update the computational task quantity f(t) of the vehicle itself, and update the computational task quantity g(t) of the other vehicles, with the following expressions:

[0115] f(t)=f(t)+τ-wk

[0116] g(t)=g(t)+w k

[0117] (4.2) If the computing node is a road domain communication computing unit node, then update the vehicle's computing task quantity f(t) and update the road domain communication computing unit's computing task quantity h(t), with the following expressions:

[0118] f(t)=f(t)+τ-w k

[0119] h(t)=h(t)+w k

[0120] Table 1. Pseudocode of the computational task allocation algorithm based on the water injection method.

[0121]

[0122]

[0123] Step 4.5: After the selected node completes the task processing, it sends the result back to the original vehicle; the specific process of step S5 is as follows:

[0124] Step 5.1: Output traffic evaluation indicators for various traffic scenarios. In this specific embodiment, the service level of the intersection basically reaches level C;

[0125] Step 5.2: Output communication evaluation indicators for various traffic scenarios, as shown in the following figures. Figure 5 As shown, Figure 5 This is a diagram showing the vehicle-road cooperative computation delay results in a specific embodiment of the present invention. Figure 5 (a) to 5(e) represent five different levels of vehicle computing power heterogeneity;

[0126] This specific embodiment illustrates that the present invention can realize the full-process simulation of the allocation, processing and feedback of computing tasks between the road domain communication computing unit and intelligent vehicles, output traffic and communication evaluation indicators under various scenarios, and verify the variation law of vehicle-road cooperative computing latency under different scenarios.

[0127] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A multi-layer intelligent agent simulation method for vehicle-road cooperative computing, characterized in that... include: The S1 basic data input module reads information data from satellite maps, road infrastructure, roadside intelligent devices, and vehicles; The S2 road scene construction module constructs road scenes; The S3 traffic operation management module constructs a traffic management model and continuously updates the management plan; The S4 vehicle-road cooperative computing module distributes, processes, and provides feedback on computing tasks. The S5 results visualization module outputs traffic and communication evaluation indicators for various traffic scenarios; In step S3, the traffic control model constructed by the traffic operation control module includes: signal control, variable speed limits, and tidal flow lanes; the process of generating the control plan includes: (1) Set the driving behavior parameters of the vehicle intelligent agent, specifically including the parameters of car-following behavior and lane-changing behavior; the initial speed and acceleration parameters of different vehicle intelligent agents follow a given distribution; (2) Construct a traffic control model, including signal control, variable speed limit, and tidal flow lanes; (3) Based on indicators such as vehicle travel delay and intersection queue length, update the control plan and its parameters; In step S4, the process of vehicle-road cooperative computing module distributing, processing, and providing feedback on computing tasks includes: (1) The vehicle intelligent agent generates a certain size of computing task at a certain frequency and includes all vehicles and road communication computing units within its communication range into the candidate computing node set; (2) Based on the water-filling method, select computing nodes from the candidate set and allocate computing tasks; the computing task allocation algorithm based on the water-filling method includes: the stage of searching for the best water-filling line; the stage of calculating the amount of tasks to be allocated; the stage of selecting cooperative computing nodes; and the stage of judging whether the task can be successfully sent and updating the amount of computing tasks. (3) After the selected node completes the task processing, it sends the result back to the original vehicle.

2. The multi-layer intelligent agent simulation method for vehicle-road cooperative computing according to claim 1, characterized in that, In step S1, the basic data input module performs the following steps: reading information data from satellite maps, road infrastructure, roadside intelligent devices, and vehicles; wherein: The basic elements of road infrastructure include materials, alignment, and signage / markings; Intelligent roadside equipment includes sensing, computing, communication, and control units; the sensing unit collects vehicle location and operating status information and transmits it to the traffic operation control module through the communication module. The vehicle information includes computing power parameters, communication range, speed, driving direction, current location, and vehicle type.

3. The multi-layer intelligent agent simulation method for vehicle-road cooperative computing according to claim 1, characterized in that, The process of constructing the road scene in step S2 by the road scene construction module includes: (1) Extract the horizontal linear features of the road based on the satellite map and perform coordinate transformation to generate a linear road network topology, i.e., the basic layer of the road infrastructure. (2) Construct a road domain communication computing unit optimization deployment model, update the model parameters to meet different smart road service needs, and generate a device layer based on point elements; (3) Import information on smart road facilities and equipment into the database; (4) A geographic information map is constructed by combining a multi-layer road network and a database to create a road scene.

4. The multi-layer intelligent agent simulation method for vehicle-road cooperative computing according to claim 1, characterized in that, In step S5, the output of the result visualization module includes: (1) Output traffic evaluation indicators for various traffic scenarios, including vehicle travel delay, intersection queue length, and road service level; (2) Output communication evaluation indicators for various traffic scenarios; In the S4 vehicle-road cooperative computing module, after the computing task is successfully assigned, it will go through four stages: sending the task to the target node, queuing the task before processing at the target node, computing and processing the task, and sending the computing result back to the original node. The system computing latency T latency The calculation formula is as follows: T latency＝ T request +T queuing +T process +T response Among them, T request For transmission delay, T queuing For the waiting delay, T process To handle latency, T response For the return transmission delay.

5. A multi-layer intelligent agent simulation system for vehicle-road cooperative computing, characterized in that... include: The system includes a basic data input module, a road scene construction module, a traffic operation management and control module, a vehicle-road cooperative computing module, and a results visualization module. The multi-layer intelligent agent simulation method for performing vehicle-road cooperative computing as described in any one of claims 1 to 4.

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