Title: Gradual Delay Differentiation in Priority Scheduling
1Gradual Delay Differentiation in Priority
Scheduling
- Tom Maertens, Joris Walraevens and Herwig Bruneel
- Ghent University (UGent)
- Department of Telecommunications and Information
Processing (TELIN) - Stochastic Modelling and Analysis of
Communication Systems (SMACS) - Sint-Pietersnieuwstraat 41, B-9000 Ghent, Belgium
2Framework
- Modern telecommunication networks are designed to
offer a wide variety of services - information access
- e-mail
- internet telephony
- file sharing
- streaming media
-
- Different services have extremely diverse
Quality-of-Service (QoS) requirements - real-time services do not tolerate delay
- non-real-time services are quite vulnerable to
loss and require a large throughput
3Service differentiation
- The traffic that flows through telecommunication
devices nowadays can thus more or less be
classified into two types - Delay as QoS-measure delay-sensitive (type-1)
traffic versus delay-tolerant (type-2) traffic - To achieve the required delay differentiation
between both types of traffic, delay-sensitive
traffic is prioritised in scheduling packets for
transmission
4Assumptions
- Physical structure of the system
- discrete time
- infinite storage capacity, divided in two
priority queues - one transmission channel
- Transmission process
- work-conserving
- single-slot transmission times
- transmissions are synchronised to the slot
boundaries
5Static priority scheduling
- Priority is always given to delay-sensitive
packets - delay-tolerant packets can only be transmitted
when there are no delay-sensitive packets present
in the system - priority levels of both types of traffic never
change during time
time
6Performance of the static priority scheduling
discipline
- Low delays for delay-sensitive packets
- Possibly excessive delays for delay-tolerant
packets, especially when the system is highly
loaded and much network traffic is
delay-sensitive
Gr!_at_
time
7Dynamic priority scheduling
- Priority levels of the two types of traffic can
change during time, so delay-tolerant packets can
also be transmitted when there are
delay-sensitive packets present in the system - Dynamic priority scheduling disciplines aim for a
more gradual delay differentiation between both
types of traffic - Two categories
- varying priority levels
- priority jumps the priority level of
delay-tolerant packets can increase in the course
of time
8Priority jumps
- Packets of the low-priority queue can jump to the
high-priority queue in the course of time - Jumped delay-tolerant packets are treated in the
high-priority queue as if they are
delay-sensitive packets - Jumps occur at the end of slots
time
9Jumping criteria to decide if and when
delay-tolerant packets jump
- A maximum queueing delay in the low-priority
queue - A queue-length-threshold for one of the queues
- A random jumping probability per time unit
- An arrival characteristic of one type of traffic
10Jumping mechanisms
- Merging the high- and low-priority queues in a
slot - every slot Merge-Every-Slot (MES)
- with a certain probability Merge-By-Probability
(MBP) - Letting only one packet jump in a slot
- always Jump-Or-Transmit (JOT)
- with a certain probability Jump-By-Probability
(JBP) - Jump in a slot also depends on the number of
arrivals - delay-sensitive (type-1) packets
Jump-If-Arrivals-of-type-1 (JIA1) - delay-tolerant (type-2) packets
Jump-If-Arrivals-of-type-2 (JIA2)
11Example Merge-By-Probability
- At the end of a slot, the total content of the
low-priority queue jumps with probability ? to
the end of the high-priority queue (i.e., both
queues are merged with probability ?)
time
12Arrival process
- Two types of packets
- type-1 delay-sensitive
- type-2 delay-tolerant
- Number of arrivals of both types of packets
(denoted by a1 and a2 respectively) - are independent and identically distributed
(i.i.d.) from slot to slot - can be correlated within one slot
13Determining the system equations
- Describe the evolution of the queue contents from
slot to - slot
- uH,k content of the high-priority queue at the
beginning of slot k - uL,k content of the low-priority queue at the
beginning of slot k
14Transforming to a functional equation
- Introducing probability generating functions
-
- Assuming that the system evolves towards a steady
state ! dropping the time index k
15Solving the functional equation
- Determining the constant U(0,0) and the functions
- U(0,z2) en U(z1,z1) leads to the joint
probability - generating function of the contents of both
queues
16Delay of a type-1 packet
- Jumps always occur at the end of a slot ! all
type-1 packets that arrive during a slot enter
the high-priority queue in front of jumping
type-2 packets - Is only determined by the content of the
high-priority queue at the moment of arrival
17Delay of a type-2 packet
- Priority scheduling new type-1 packets can
arrive while type-2 packets are waiting in the
low-priority queue, and these type-1 packets have
priority - Jumping mechanism type-2 packets can jump to the
high-priority queue in the course of time - Combination of these two characteristics of the
model makes the analysis not always
straightforward!
18Results
- Probability generating functions of
- the contents of the two priority queues
- the delays of both types of packets (for most
models) - Performance measures
- moments via the moment generating property of
probability generating functions - approximate tail distributions via the
dominant-singularity method applied on
probability generating functions ? not
necessarily exponentially decaying tail
probabilities
19Numerical examples packet switch
- Arrival at an input port
- occurs with probability ?T ( arrival rate)
- and is of type 1 with probability ? ( fraction
of type-1 arrivals in the overall traffic mix) - Uniform and independent routing towards the
output ports
20Mean delays of both types of traffic for ?T0.9
21Mean delays of both types of traffic for ?T0.9
22Conclusions
- Priority schemes with priority jumps build upon
the simplicity and efficiency of the static
priority scheme, but prevents delay-sensitive
traffic from starving - Depending on the delay requirements of the
different types of traffic, we can introduce and
tailor one of the jumping mechanisms - Analysis based on probability generating
functions - can overcome mathematical challenges (e.g., the
calculation of boundary functions) - is useful for the calculation of different
performance measures (such as moments and tail
probabilities)