By U. Narayan Bhat

This introductory textbook is designed for a one-semester path on queueing conception that doesn't require a path in stochastic strategies as a prerequisite. via integrating the mandatory heritage on stochastic procedures with the research of types, this e-book presents a foundational creation to the modeling and research of queueing platforms for a huge interdisciplinary viewers of scholars. Containing routines and examples, this quantity can be used as a textbook by way of first-year graduate and upper-level undergraduate scholars. The paintings can also be precious as a self-study reference for purposes and additional learn.

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**Example text**

In other words, we are ﬁtting a straight line to the (exam 1, exam 2) pairs in our data. This is done through a classic least-squares method. ) Note that the exam 1 scores, which are stored in the ﬁrst column of our data frame, are collectively referred to as examsquiz[,1]. Omission of the ﬁrst subscript (the row number) means that we are referring to an entire column of the frame. The exam 2 scores are similarly referenced. So, our call to lm() above predicts the second column of examsquiz from the ﬁrst.

3 Introduction to Functions As in most programming languages, the heart of R programming consists of writing functions. A function is a group of instructions that takes inputs, uses them to compute other values, and returns a result. As a simple introduction, let’s deﬁne a function named oddcount(), whose purpose is to count the odd numbers in a vector of integers. Normally, we would compose the function code using a text editor and save it in a ﬁle, but in this quick-and-dirty example, we’ll enter it line by line in R’s interactive mode.

This is typical R. The same is true for this expression, on line 9: mean(abs(pred-x[(k+1):n])) Here, pred contains the predicted values, while x[(k+1):n] has the actual values for the days in question. Subtracting the second from the ﬁrst gives us values of either 0, 1, or −1. Here, 1 or −1 correspond to prediction errors in one direction or the other, predicting 0 when the true value was 1 or vice versa. Taking absolute values with abs(), we have 0s and 1s, the latter corresponding to errors. So we now know where days gave us errors.