INTRODUCTION

Equinix, Inc. is an American public corporation that provides carrier-neutral data centers and internet exchanges. Equinix provides network-neutral data centers (IBX or "Internet Business Exchange") and interconnection services. The company offers colocation, traffic exchange and outsourced IT infrastructure solutions to enterprises, content companies, systems integrators and over 950 network service providers worldwide.
Equinix currently operates 100 data centers across 32 major metropolitan areas in 15 countries in North America, Europe, Asia-Pacific and South America. The company has its headquarters in Redwood City, California, United States. According to the company website, Equinix’s mission is to “store, power, and connect the internet.”
What Makes a Data Center an Equinix IBX Data Center
Every Equinix International Business Exchange™ (IBX®) data center delivers operational expertise, standards compliance and physical security to safeguard your valuable information.
Peace of Mind When you Need it Most * Reliability – All Equinix IBX data centers are equipped with full UPS power, back-up systems, and N+1 (or greater) redundancy, with a proven, industry-leading >99.999% uptime record. * Power Density – With robust heating, ventilation, and air conditioning (HVAC) systems, Equinix IBX data centers exceed the requirements of even the most power-hungry deployments. * Security – Each Equinix IBX data center utilizes an array of security equipment, techniques and procedures to control, monitor and record access to the facility, including individual cages. * Recovery – IBXflex™ Space provides operations centers and storage space when you need it; Equinix Smart Hands™ offers 24-hour access to qualified technical support – with Equinix, you can maintain your mission-critical operations and equipment under any circumstances.
Make the connections that will drive growth.

Data Center expertise that goes beyond space and power.
Our technical experts have configured some of most complex installations for the world’s most demanding businesses. In addition to recommending cage, suite and power solutions to meet your physical security and power requirements, we’ll also facilitate interconnection with your industry’s digital ecosystem.

II. SITUATIONAL PROBLEM

Base on the monthly reports of the Operational Manager’s of Equinix, The work force estimates that cases will arrive at the rate of 45 per hour. The Call Center Professional that is on shift can service cases at the rate of five every six minutes.

Assuming Poisson arrivals and exponential service, find the following.

1. Utilization of the service attendant 2. Average number in the waiting line (cases) 3. Average number in the system (cases) 4. Average waiting time in line 5. Average waiting time in the system, including the service 6. Probability that the service is empty

III. SOLUTION

λ (lambda) = means arrival rate per unit of time ( average arrival rate of customers) μ (moo) = means service rate per unit of time (average service rate of servers)
Lq = means number in queue (average number of customers in queue)
Ls = means number in system (average number of customers in queue including number being served)
Wq = means time in queue (average time of waiting in queue)
Ws = means time in system (average time of waiting in queue plus service time)
Pw= probability that the service is busy (utilization factor)

We have to identify the average number of cases arriving at a certain period and also the number of cases that can be accommodated by the Call Center Professional. In the problem the arrival rate is denoted by λ = 45 cases per hour and the service rate denoted by the symbol μ = 50 cases per hour ( five every 6 minutes = 56*60=50. It is important that the unit of time of arrival and service rate must be the same.

1. Utilization of the service attendant refers to the probability that the service facility is busy.
Pw = λu = 4550 = 90%
The 90% utilization of the service attendant means that the server is busy in 7.2hours or 7 hours and 12mins for every 8 hours of his working time in which he can spend the excess time to other productive work.

2. Average number in the system refers to the number of customers waiting to be served including the one receiving the service.
Lq = λ2uu-λ = 4525050-45 = 8110 = 8.1 cases 3. Average number in the system refers to the number of cases waiting to be served including the one receiving the service.
Ls= λu-λ = 4550-45 = 9 cases 4. Average waiting time in line or average waiting time in queue
Wq = λuu-λ = 455050-45 = 950 = 0.18 x 60 = 10.8 (.8 x 60 = 48 secs) = 10mins and 48 seconds. 5. Average waiting time in the system refers to the time that the customer will spend while waiting in the queue and getting the service.
Ws= 1u-λ = 150-45 = 15 =.20 hours or 12 minutes
This means that it will take an average of 12 minutes for the case to be resolved. 6. Probability that the service facility is empty
Po = 1 – Pw or 1- λu = 1- 4550 1-.90 = 110 or 10%

This means that the probability of the server without customer within the eight-hour working time is 10% or this is equivalent to 48minutes for every eight hours on the average.