Question

In: Statistics and Probability

There are two servers. Hiba has just started service at server 1, while Daniella has just...

There are two servers. Hiba has just started service at server 1, while Daniella has just started service at server 2. Hiba’s service time at server 1 is exponentially distributed with mean 1/4 hour. Daniella’s service time at server 2 is exponentially distributed with mean 1/6 hour. Daniella’s service time and Hiba’s service time are independent.

(a) What is the probability that Hiba finishes service before Daniella?

(b) What is the expected time in minutes until the first person finishes?

(c) What is the expected time in minutes until the second person finishes

Solutions

Expert Solution


Related Solutions

A small company network have multiple servers (including a web server, a log server, DNS servers,...
A small company network have multiple servers (including a web server, a log server, DNS servers, a file server for inventory information and customer orders, but no email server) , two firewalls, DMZ, and PCs. The company sales products online. a). Suppose that you are a system administrator. What types of network connections will you allow to be established with the servers in the DMZ from the Internet? b). What are the points of entry for attackers? c). How do...
Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential...
Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential rates μ1 and μ2, with μ1 > μ2. If server 1 becomes idle, then the customer being served by server 2 switches to server 1. a) Identify a condition on λ,μ1,μ2 for this system to be stable, i.e., the queue does not grow indefinitely long. b) Under that condition, and the long-run proportion of time that server 2 is busy.
Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential...
Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential rates µ1 and µ2, with µ1 > µ2. If server 1 becomes idle, then the customer being served by server 2 switches to server 1. a) Identify a condition on λ, µ1, µ2 for this system to be stable, i. e., the queue does not grow infinitely long. b) Under that condition, find the long-run proportion of time that server 2 is busy.
A server is a computer or device on a network that manages network resources. Servers are...
A server is a computer or device on a network that manages network resources. Servers are often dedicated, meaning that they perform no other tasks besides their server tasks. On multiprocessing operating systems however, a server may be one of several programs that are each managing specific requests for services from clients or a particular hardware or software resource, rather than the entire computer. For each of the server types below, provide a short description of the service each provides...
Consider three servers. An average of 12 customers per hour arrive from outside at server 1,...
Consider three servers. An average of 12 customers per hour arrive from outside at server 1, an average of 36 customers per hour arrive from outside at server 2 and an average of 24 customers per hour arrive from outside at server 3. Interarrival times are exponential. Servers 1, 2 and 3 can serve at exponential rates of 100, 120 and 80 customers per hour respectively. After completing service at server 1, 25% of the customers leave the system and...
Outline the necessary actions that Server Administrator's must verify for proper operation of servers in the...
Outline the necessary actions that Server Administrator's must verify for proper operation of servers in the event of a failover/redundancy plan.
1.14. A service facility consists of two servers in series (tandem), each with its own FIFO...
1.14. A service facility consists of two servers in series (tandem), each with its own FIFO queue (see Fig. 1.50). A customer completing service at server 1 proceeds to server 2, while a customer completing service at server 2 leaves the facility. Assume that the interarrival times of customers to server 1 are IID exponential random variables with mean 1 minute. Service times of customers at server 1 are IID exponential random variables with mean 0.7 minute, and at server...
Discuss different service-based server operating systems, server computers, and server software that a network administrator must...
Discuss different service-based server operating systems, server computers, and server software that a network administrator must choose between. Applied Concepts (AC) - Week/Course Learning Outcomes Using your textbook, LIRN-based research, and the Internet, apply the learning outcomes for the week/course and lecture concepts to one of the following scenarios: As applied to your current professional career As applied to enhancing, improving, or advancing your current professional career As applied to a management, leadership, or any decision-making position As applied to...
A financial planner is advising two clients, Daniel and Tracy. Daniel has just started to work...
A financial planner is advising two clients, Daniel and Tracy. Daniel has just started to work full time; Tracy is 60, has been working full time and planning to retire in 5 years. How would their investment policy statements (IPS) be affected by their own situations, and how will their IPS’s return and risk objectives and asset allocation be different?
1. A single-server queueing system has an average service time of 16 minutes per customer, which...
1. A single-server queueing system has an average service time of 16 minutes per customer, which is exponentially distributed. The manager is thinking of converting to a system with a constant service time of 16 minutes. The arrival rate will remain the same. The effect will be to: increase the utilization factor. decrease the utilization factor. decrease the average time in the system. Increase the average time in the system. not have any effect since the service time is unchanged....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT