A grid is an open system, a large collection of autonomous systems giving individual users the image of a single virtual machine with a rich set of hardware and software resources. The crest aim of a Grid is to allocate best resource to a job by comparing the user requirements with the resource capabiliities. The process of selecting resources based on user requirements is called "resource matching". In Grid environment the resource pool is highly dynamic. The user behavior in the Grid environment is also cannot be predicted. While matching the job with the resources, the average response time to find the best match depends upon the arrival rate of the job and the resources. The average response time to find the best match can be increased by increasing the service rate of the Grid. The service rate of the Grid can be increased by having two queues in the Grid. This paper deals with the impact of time varying arrival rate of job, a large time varying arrival rate of resource, number of queues, in matching the user requirements with the resource capabilities. The arrival rate of job and the resource would require to be in a fashion that the average response time of the job should get minimized.