To decrease the queue mean time, additional resources must be added in the service side which can increase the service cost.

Explanation:

Queuing theory is the study of queues or waiting lines. It is used to analyze and design systems where customers or jobs arrive at a facility and wait in line to be served by a server. Queuing systems are used in various applications such as telephone call centers, banks, hospitals, and manufacturing systems. The cost of providing service in a queuing system depends on various factors such as the arrival rate of customers, the mean time in the queue, the number of servers, and the service rate.

In this question, we are asked to determine the factor that increases the cost of providing service in a queuing system. Let's examine each option:

a) Increased mean time in the queue - When the mean time in the queue increases, it means that customers are waiting longer to be served. This can lead to customer dissatisfaction and can result in lost business. However, it does not necessarily increase the cost of providing service. In fact, if the number of servers remains the same, the cost of providing service may decrease as the server utilization decreases.

b) Increased arrival rate - When the arrival rate of customers increases, it means that there are more customers in the system. This can lead to longer queues and increased waiting times. This can result in customer dissatisfaction and lost business. However, it does not necessarily increase the cost of providing service. In fact, if the number of servers is increased to handle the increased arrival rate, the cost of providing service may remain the same.

c) Decreased mean time in the queue - When the mean time in the queue decreases, it means that customers are waiting less to be served. This can lead to increased customer satisfaction and can result in increased business. However, it can also increase the cost of providing service. This is because when the mean time in the queue decreases, the server utilization increases. This means that the servers are being used more frequently, which can lead to increased maintenance and operating costs.

d) Decreased arrival rate - When the arrival rate of customers decreases, it means that there are fewer customers in the system. This can lead to shorter queues and decreased waiting times. This can result in increased customer satisfaction and can result in increased business. However, it does not necessarily decrease the cost of providing service. In fact, if the number of servers remains the same, the cost of providing service may increase as the server utilization decreases.

Therefore, the correct answer is option 'C' - Decreased mean time in the queue. When the mean time in the queue decreases, it can increase the cost of providing service due to increased server utilization.