Telecommunication Networks - formulario ed esercizi

Message delivery time with CS connections

T = ^M/_R + Bt_p + N1c

• 1_c = switching time
• t_p = propagation time
• N = # of intermediate switches
• M = message length

Message delivery time with PS connections

T = ^N-M+1/_R + t_p + N1c

Message delivery time with PS + PIPELINE

T = t_p + N t_c + (N-A) ^M/_R + ^K/_R + ^K+M/_R

Message delivery time with PS + PIPE + Bottleneck

T = t_p + N t_c + (^K/_R) ⁴/_{∑h≠Δ1/Bh} ^K+M

• h = index of bottleneck link

Optimal K with bottleneck

K = √^M/_H ∑^R_h/_h≠Δ1/B^h

BDP

R = delay

Delay = RT ⇒ PIPE CAPACITY

Delay_end-to-end ⇒ # bits can be transmitted simultaneously

• Bit rate R_o
• Throughput S ⇒ S_g ≤ S ≤ R_o
• S_g = S ⋅ I_OUT/I_INPUT
• = S ⋅ OVERHEAD

POISSON P_X(n) = ^λn/_n! . e^-λ E(n) = λ

GEOMETRICA P_X(n) = p(1-p)^n-1 . p succ. prova.

ESPOENZIALE ƒ_X(x) = μ e^-μx E(x)= ¹/_μ

Configure the network with the following services:

• Web page
• e-mail
• Internet cloud service
• 3 private sub-networks of ~100 networks each, which should be able to freely communicate with one another, access the web and mail server of the company, and access the public Internet only for HTTP services.

1. What is the smallest block of public IP addresses that the company needs to acquire?
2. Which other devices are needed to configure the network?
3. Draw schematically the connections among the network devices and assign IP addresses and network functionalities to all the devices.
4. Write the routing/NAT tables when needed.

LAN A: 192.168.1.0/25

LAN B: 192.168.2.0/25

LAN C: 192.168.3.0/25

DHCP: 192.168.1.253

We need public IP address for:

• DNS, WEB, MAIL, R2 eth1 (NAT) R1 eth0

We need at least a block of size 8, e.g.

1. 1.255.255.254/29 WEB
2. 1.255.255.255/30 MAIL
3. 2.255.255.0/29 DNS
4. 2.255.255.252/31 R1 eth0
5. 1.255.255.255/28 (for all other network use)

1)

Consider a Token Bucket Filler used as Traffic policer. Assume that each token is worth the transmission of one pack of L bits.

Find the token bucket parameters that give an average rate R and a peak rate R_p for a time T_burst.

Policer g_t = ^R/_L average token rate

bucket size

b = (^{(R_p - R)}/_gt) T_burst

= (^{(R_p - R)}/_L) T_burst

2)

Assume that packets arrive to the TBF according to a Poisson process of rate λ = 0.1;

g_t = A new token is generated every T seconds starting from time t₀

If at time t₀ = T_k, the bucket is empty, what is the probability that the next packet is marked by the TBF as "excess"?

Solution

The time to get a new token is T_n = ¹/_gt. Since the packet arrival process is Poissonian, the inter-arrival times are i.i.d exponential random variables (of parameter λ) and hence are memoryless (which means that the time before the next arrival starting from t₀ = T_k is still exponentially distributed with parameter λ

irrespective of the time elapsed since the previous arrival at time t₀)

Therefore the next pack will be marked as "excess" if it arrives before