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Gradual Delay Differentiation in Priority Scheduling

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Priority is always given to delay-sensitive packets: ... A random jumping probability per time unit. An arrival characteristic of one type of traffic ... – PowerPoint PPT presentation

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Title: Gradual Delay Differentiation in Priority Scheduling


1
Gradual 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

2
Framework
  • 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

3
Service 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

4
Assumptions
  • 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

5
Static 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
6
Performance 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
7
Dynamic 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

8
Priority 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
9
Jumping 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

10
Jumping 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)

11
Example 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
12
Arrival 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

13
Determining 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

14
Transforming to a functional equation
  • Introducing probability generating functions
  • Assuming that the system evolves towards a steady
    state ! dropping the time index k

15
Solving 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

16
Delay 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

17
Delay 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!

18
Results
  • 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

19
Numerical 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

20
Mean delays of both types of traffic for ?T0.9
21
Mean delays of both types of traffic for ?T0.9
22
Conclusions
  • 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)
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