What does the Pollaczek- Khinchin (P-K) formula explain in an M/G/1 system? Write the P-K formula and use it to show the average number of customers in the M/G/1 queuing system (including customers in the queue and in service). What does the Pollaczek- Khinchin (P-K) formula explain in an M/G/1 system? Write the P-K formula and use it to show the average number of customers in the M/G/1 queuing system (including customers in the queue and in service).
Problem 29. Suppose 1 < p < 00 and f, g E IP(X, M,). Suppos lfllp and |gl|p are nonzero, and lfgllp llfllp+ llgllp Prove that a.e 19llp Problem 29. Suppose 1
The M/M/1 and M/M/1/K queuing system: Consider the M/M/1 and M/M/1/K queuing systems [see in class notes]. For the M/M/1/K system show that, for ρ < 1, in class notes: p" (1-p) п-0, 1,2, ..., К-1; р-— 1-р*а п, K+1 и N- Р_(К+1)pku К-+1 1-р*а 1-р M/M/1 Queuing System with Finite Capacity (M/M/1/K) Systems have a finite capacity for serving customers. The M/M/1 queuing system capable of supporting up to K customers is called an M/M/1/K queuing system. Arrivals at...
Use the recurrence relation (l1)P+1-(21 +1)xP IP-1 to compute 70r15a)] Also, directly compute P6() and P(). [P(x)63r to show their orthogonality P)P4(x) da
4. [10 pts] Define T: P2 → Max2 by T(p)=Ip(0) p(-1) 10(1) p(2) (a) Show that T is a linear transformation. (b) What is the kernel of T? (e) Describe the range of T as the set of 2 x 2 matrices with the entries a,b.c,d satisfying certain conditions. Hint: Work on the practice problem §4.231 first. For finding the kernel, you may use the fact that if a polynomial p has degree at most 3 and p(0) = p(-1)...
SHOW ALL WORK. ANSWER A AND D m produces a IP A two-slit experiment with slits separated by 4.9x10 second-order maximum at an angle of 0.0990". Part A Find the wavelength of the light used in this experiment. Express your answer using two significant figures. num Submit Request Answer Part B Part C Part D Calculate the wavelength for a slit separation of 6.5x104m. Express your answer using two significant figures. 40 AEO O ? nm Submit Request Answer
a) Discuss why the de Broglie wavelength λ corresponding to a momentum p (p wavenumber given by k # 2n/A) leads to a representation of p by the operator p as (h/) (d/dx) hk, where k is the b) Using theoperao orm of p given in part a, show that,pih c) The total energy of a simple harmonic oscillator of mass M and spring constant K can be written as H- p2/M + ke . If the mass is displaced...
Question-5 (20%): 1.6 m M=15 Nm k = 60 N/m The 20-kg rod is released from rest when 0 = 0°.In the shown direction a moment of 15 Nm is applied. Determine the angular velocity of the rod when 0 = 90'. The unstretched length of the spring is 0.25 m. Note that 1. m1
2. Show that p-1 E(+1) = 2a +(*)(4+1) k=0 l=0 Hint: Fix an 0 <I<p – 1, Ask youself how many k satisfy k2 = 1 mod p.