API

The main algorith offered by the Queuinx is queuinx.RouteNetStep() that operates on queuinx.Network objects.

queuinx.RouteNetStep(update_flow_fn, update_queue_fn, reducers)

Returns a function that applies a step of configured model

Parameters:

update_flow_fn (Callable[[RaggedCarry, Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]]], Tuple[RaggedCarry, Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]]]]) – function implementing scan like operation over the queues along a flow
update_queue_fn (Callable[[Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]], Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]], Array, Array], Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]]]) – function used to update the queues
reducers (Any) – A tree of callable used to reduce the flows

Returns:

A function that applies a step of configured model

Return type:

Callable[[Network], Network]

class queuinx.Network

Class for keeping track of a queuing network.

Parameters:

queues – The queues feature e.g. buffer size or service rate. It is a (nested) vector of shape [n_queues] + queue_shape, where n_queues=sum(net.n_queues)
flows – The flows features, e.g. traffic properties. It is a (nested) vector of shape [n_flows] + queue_shape, where n_flows=sum(net.n_flows)
flow – The indices of the flows
step – The position of :ref queue: in the flow :param flow:
queue – The indices of the queues
n_flows – The number of flows per network. It is a vector of integers of shape [sum(net.n_flows)]
max_path_length_mask – The mask of the maximum path lengths. It a boolean matrix of shape [n_graph,max_path_length]. The number of consecutive True encodes the maximum path length for the subnetwork.
n_queues – The number of queues per network. It is a vector of integers of shape [n_graph]
n_routes – The number of route entries (len(net.flow) per network. It is a vector of integers of shape [n_graphs]
interface – Interface the queue belongs that groups queues e.g. for scheduling. It is either None or a vector of shape [sum(n_queue),1]
n_interfaces – The number of interfaces per network. It is a vector of integers with shape [n_nets], such that network.n_interfaces[i] is the number of interfaces in the i-th network.

__init__(queues, flows, flow, step, queue, n_flows, max_path_length_mask, n_queues, n_routes, interface=None, n_interfaces=None)

Parameters:

queues (Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]]) –
flows (Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]]) –
flow (Array | ndarray | bool_ | number) –
step (Array | ndarray | bool_ | number) –
queue (Array | ndarray | bool_ | number) –
n_flows (Array | ndarray | bool_ | number) –
max_path_length_mask (Array | ndarray | bool_ | number) –
n_queues (Array | ndarray | bool_ | number) –
n_routes (Array | ndarray | bool_ | number) –
interface (Array | ndarray | bool_ | number | None) –
n_interfaces (Array | ndarray | bool_ | number | None) –

Return type:

None

property flow_lengths: Array | ndarray | bool_ | number

Dynamic length of each flow in the network

Returns:: An array of flow lengths

On top of this core functionality a rich set of algorithm is built.

A library of RouteNet based models.

class queuinx.models.FiniteFifo

Parameters and state of fine fifo buffer

__init__(b, service_rate, arrivals, pasprob)

Parameters:

b (Array | ndarray | bool_ | number) –
service_rate (Array | ndarray | bool_ | number) –
arrivals (Array | ndarray | bool_ | number) –
pasprob (Array | ndarray | bool_ | number) –

Return type:

None

class queuinx.models.PoissonFlow

Parameters and state Poisson arrival flow

__init__(rate)

Parameters:: rate (Array | ndarray | bool_ | number) –
Return type:: None

class queuinx.models.QoS

QoS parameters

Parameters:

delay – An expected delay including queuing and service time
jitter – Variance of waiting and service time
loss – Job loss probability

__init__(delay, jitter, loss)

Parameters:

delay (Array | ndarray | bool_ | number) –
jitter (Array | ndarray | bool_ | number | None) –
loss (Array | ndarray | bool_ | number) –

Return type:

None

queuinx.models.Readout_mm1b(buffer_upper_bound)

Computes delay per path assuming M/M/1/B delay model

Parameters:: buffer_upper_bound (int) –
Returns:: A step function performing computations.
Return type:: Callable[[Network], Network]

queuinx.models.RouteNetStep(update_flow_fn, update_queue_fn, reducers)

Returns a function that applies a step of configured model

Parameters:

update_flow_fn (Callable[[RaggedCarry, Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]]], Tuple[RaggedCarry, Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]]]]) – function implementing scan like operation over the queues along a flow
update_queue_fn (Callable[[Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]], Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]], Array, Array], Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]]]) – function used to update the queues
reducers (Any) – A tree of callable used to reduce the flows

Returns:

A function that applies a step of configured model

Return type:

Callable[[Network], Network]

Queuing theory

For analytical results Queuinx provides set of queuing theory functionalities.

MM1b

Numerical procedures for M/M/1/b system

class queuinx.queuing_theory.mm1b.StationarySystem

A Stationary distribution of system occupancy in M/M/1/b

__init__(rho, b, buffer_upper_bound)

Parameters:

rho (Array | ndarray | bool_ | number) – System utilization
b (Array | ndarray | bool_ | number) – buffer size
buffer_upper_bound (int) – Statically known upper bound on the buffer.

mean(): Calculates the mean.

variance(): Calculates the variance.

queuinx.queuing_theory.mm1b.delay_distribution(a, mu, b, buffer_upper_bound)

Return delay distribution as distrax.Distribution.

Parameters:

a (Array | ndarray | bool_ | number) – Arrival rate
mu (Array | ndarray | bool_ | number) – Service rate
b (Array | ndarray | bool_ | number) – buffer
buffer_upper_bound (int) – Static integer bounding all-buffers

Returns:

Delay distribution (including service time)

Return type:

Distribution

MM1

queuinx.queuing_theory.mm1.delay_distribution(a, mu)

Return delay distribution in M/M/1 for customers who arrive and find the queue as a stationary process [1]. This includes both waiting and service time.

Parameters:

a (Array | ndarray | bool_ | number) – Arrival rate
mu (Array | ndarray | bool_ | number) – Service rate

Returns:

Delay distribution (including service time)

Return type:

Distribution | Distribution

Basic(fluid)

Utilities

Queuinx provides few utility functions mostly for avoiding recompilation due to changing shapes.

class queuinx.utils.RaggedCarry

Carry for variable length sequences. Svan function must be decorated with ragged()

__init__(carry, step, n_step)

Parameters:

carry (Array | ndarray | bool_ | number | Iterable[Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]] | Mapping[Any, Array | ndarray | bool_ | number | Iterable[ArrayTree] | Mapping[Any, ArrayTree]]) –
step (Array | ndarray | bool_ | number) –
n_step (Array | ndarray | bool_ | number) –

Return type:

None

queuinx.utils.batch(nets)

Returns a batched network given a list of networks.

Parameters:: nets (Sequence[Network]) –
Return type:: Network

queuinx.utils.ragged(f)

Decorates scan function to make it compatible with RaggedCarry

Parameters:: f (Callable) – A scan function
Returns:: A function accepting RaggedCarry

queuinx.utils.unbatch(net)

Returns a list of networks given a batched network.

Parameters:: net (Network) – the batched network, which will be unbatched into a list of networks.
Return type:: list[Network]

Experimental

Experimental models models.

queuinx.experimental.models.ApproximateScheduling(n_tos, buffer_upper_bound, interface_upper_bound)

Queuing model with scheduling.

Parameters:

n_tos (int) – Maksimum number of types of service per queue group
buffer_upper_bound (int) – Statically know limit for all buffers
interface_upper_bound (int) – Statically know limit for number of interfaces

Return type:

Callable[[Network], Network]

queuinx.experimental.models.FixedPoint(model, *args, **kwargs)

Wraps model to return a function computing fixed point solution

Parameters:

model – Model function i.e. this function should return a single step of routenet
args – list of arguments for jaxopt.FixedPointIteration
kwargs – dict of arguments for jaxopt.FixedPointIteration

Returns:

A model computing fixed point the given model.

class queuinx.experimental.models.PacketFlow

Flow with information about packet length

__init__(rate, plen, weighted_plen=None)

Parameters:

rate (Array | ndarray | bool_ | number) –
plen (Array | ndarray | bool_ | number) –
weighted_plen (Array | ndarray | bool_ | number | None) –

Return type:

None

class queuinx.experimental.models.PacketQueue

Queue with scheduling

__init__(b, service_rate, arrivals, pasprob, speed, w, priority, bit_buffer, policy=4)

Parameters:

b (Array | ndarray | bool_ | number) –
service_rate (Array | ndarray | bool_ | number) –
arrivals (Array | ndarray | bool_ | number) –
pasprob (Array | ndarray | bool_ | number) –
speed (Array | ndarray | bool_ | number) –
w (Array | ndarray | bool_ | number) –
priority (Array | ndarray | bool_ | number) –
bit_buffer (Array | ndarray | bool_ | number) –
policy (int) –

Return type:

None

queuinx.experimental.models.Readout_mm1()

Calculates QoS based on MM1 approximation

Returns:: RouteNet step callable
Return type:: Callable[[Network], Network]

enum queuinx.experimental.models.SchedulingPolicy(value)

Types of scheduling

Valid values are as follows:

SP = <SchedulingPolicy.SP: 1>

WFQ = <SchedulingPolicy.WFQ: 2>

DRR = <SchedulingPolicy.DRR: 3>

FIFO = <SchedulingPolicy.FIFO: 4>