Assignment 3 Network wide Max-Min Allocation

Question 1 [10 points] (Network wide Max-Min Allocation)
Consider the network shown in the picture above. Assume that all network links (Link 1,
2 and 3) have equal bandwidth (1 unit each). Connections are setup between source
destination pairs (Si, Di) for communication. Assume that all connections have equal
weights and sources are not constrained (i.e., they can transmit at whatever the rate the
switching elements can assign).
1. What would be bandwidth allocated connections at each of the links (local
allocation) if network wide allocation for the flows is not considered?
2. What would be bandwidth allocated connections at each of the links if network
wide max-min bandwidth allocation is considered?
Question 2 [5 points] (RED)
A router uses a single queue for AF service. All three classes (AF1x, AF2x and AF3x) and
colors (x=1 for green, x=2 for yellow and x=3 for red) are to be supported.
1. Design a RED drop probability scheme (graph) such that the relative orders of
class (priority order AF1, AF2 and AF3) and color (priority order green, yellow
and red) are always maintained when dropping packets. You don’t need to
maintain same minTh and maxTh for each class.
2. Design a RED drop probability scheme (graph) such that the relative orders of
class (priority order AF1, AF2 and AF3) and colors are maintained but colors
belonging to different classes are mapped to the same drop probability curve
Switching
Element
1
Switching
Element
3
Switching
Element
2
S1 ... S16
S17 S19
D1 ... D14 D15 ... D18
Link 1 Link 2 Link 3
S20 ... S26
Switching
Element
4
D19 ... D26
...(e.g., AF12, AF21; AF13, AF22, AF31; AF23, AF32; etc). Design this scheme with
the same minTh and maxTh for all classes.
Question 3 [25 points] (Traffic Marking)
A constant bit rate (CBR) connection contracts a peak rate (PIR) of ¼ of line rate with a
network (i.e., PIR=1/4 Line rate). Assume the average packet size is 500 bytes. The
network provider decides to mark the traffic with a single rate three color marker
(srTCM) with CBS=500 bytes and EBS=100 bytes (allows some jitter). For simplicity you
can assume that the Line rate is 1 byte/sec. The purpose of this question is to verify the
working of srTCM algorithm in the following scenarios when a user sends conforming
and non-conforming traffic. Your goal is to test the outcome of srTCM and check the
marked traffic. The purpose is also to test parameter settings. You can consider up to 40
packet transmissions. The scenarios are:
1. Connection sends traffic at exactly the peak rate
2. Connection sends traffic at 1.5 times the peak rate (contract violation)
3. How will your answer for part (2) change if EBS=500 bytes?
4. If CBS set to 250 and EBS=100, what will be the outcome for part (1)?
5. What is your inference about the bucket settings on marking?
Question 4 [10 points] (EBW)
Consider the Equivalent Bandwidth (EBW) equation of Gibbens and Hunt (GH) (slide 19
of Admission Control). A switch uses two separate queues (of different lengths) for two
classes of traffic, each requiring a different packet loss ratio (CLR), say 10-7 and 10-5. For
the same traffic parameters (PCR, SCR, ABS), prove that the number of connections
admitted would be the same for both queues, if log(Cell Loss Ratio) and Buffer are
provisioned in the same proportion in both queues. Verify your answer with an example
of PCR=1.0, SCR=0.3, ABS=10. What do you infer from this? How much bandwidth is
allocated if we use Robert’s Heuristic (slide 18 of Admission Control) instead of GH?
Question 5 [10 points] (Multi-class EBW in a single queue)
A switch uses a single queue for three different traffic classes EF, AF and BE at a link of
capacity 1.0. The switch admits 10 EF services (peak rate of 0.01); 20 services of AF (with
a peak rate of 0.01, average rate of 0.001, average burst size of 10 packets, buffer size of
1000 packets, packet loss ratio of 10-7) and 100 services of BE with a minimum rate of
0.001. Assume that the average packet size is 100 bytes for all services.
1. What’s the remaining (available) bandwidth on the link?
2. What’s the Statistical gain achieved for VBR services?
3. What is the load (utilization) on the switch?
4. What will the delay experienced by these packets when traversing through the
switch?Question 6 [10 points] (Multi-class EBW)
Please refer to Question 5. Let us assume that the switch is now replaced with a newer
switch that uses three separate queues for EF, AF and BE traffic and has WFQ packet
scheduler at a link of capacity 1.0. The switch sets weights of 20, 40 and 40 to these
queues. Assume the same set of admitted services as in Question 5.
1. What is the load on EF queue?
2. What is the load on AF queue?
3. What is the load on BE queue?
4. Assuming that the unallocated bandwidth for EF and AF is given to BE queue by
the WFQ, what will be the bandwidth achieved by the BE queue?
5. [6 points] As each queue can get its dedicated bandwidth, for now model each
queue independently with that allocated bandwidth as an M/M/1 queue. With
this assumption what would be the delay experienced by packets when
traversing these queues? How does it compare with Question 5?
Question 7 [6 points] (Multi-class EBW)(For CSC 567 Only)
Repeat Question 6 part 5 with the assumption that the switch uses a priority queueing
instead of WFQ. What would be delays experienced by each of the services?