Minimizing Mean Response Time In Batch-Arrival Non-Observable Systems With Single-Server FIFO Queues Operating In Parallel

2021 ◽  
Author(s):  
Mikhail Konovalov ◽  
Rostislav Razumchik
Keyword(s):  
Response Time ◽  
Arrival Time ◽  
Time Instant ◽  
Single Server ◽  
State Information ◽  
Mean Response Time ◽  
Routing Policy ◽  
Long Run ◽  
Service Rates ◽  
Routing Policies

Consideration is given to a dispatching system, where jobs, arriving in batches, cannot be stored and thus must be immediately routed to single-server FIFO queues operating in parallel. The dispatcher can memorize its routing decisions but at any time instant does not have any system's state information. The only information available is the batch/job size and inter-arrival time distributions, and the servers' service rates. Under these conditions, one is interested in the routing policies which minimize the job's long-run mean response time. The single-parameter routing policy is being proposed which, according to the numerical experiments, outperforms best routing rules known by now for non-observable dispatching systems: probabilistic and deterministic. Both the batch-wise and job-wise assignments are studied. Extension to systems with unreliable servers is also addressed.

Customer routing to different servers with complete information

1989 ◽  
Vol 21 (4) ◽  
pp. 861-882 ◽  
Author(s):  
Zvi Rosberg ◽  
Parviz Kermani
Keyword(s):  
Complete Information ◽  
Service Rate ◽  
Dependent Rate ◽  
Routing Policy ◽  
State Dependent ◽  
Long Run ◽  
Ideal Situation ◽  
Ideal System ◽  
Holding Cost ◽  
Routing Policies

In this paper we consider a queueing system having n exponential servers, each with its own queue and service rate. Customers arrive according to a Poisson process with rate λ, and upon arrival each customer must be routed to some server's queue. No jockeying amongst the queues is allowed and each server serves its queue according to a first-come-first-served discipline.Each server i, 1 ≦ i ≦ n, provides service with a state-dependent rate μ(i)(k), k = 0, 1, …. In addition, at every queue i, there is a deterministic holding cost which occurs at rate h(i)(k) while there are k customers at the queue.An admissible routing policy is a policy that assigns each arriving customer to one of the queues. A decision at time t may be randomized and dependent on the queue lengths and decisions till time t. An optimal routing policy is an admissible policy that minimizes the long-run average holding cost.In this study, we bound the optimal cost from below, by considering an ideal system, where each server optimally selects a given proportion of customers, irrespective of other servers' selections. From this ideal system we construct a class of admissible routing policies, the overflow routing class, that approximates the ideal situation for each server. Finally, we evaluate the policies and compare them to the lower bound.

The Downs-Thomson Effect in a Markov Process

1997 ◽  
Vol 11 (3) ◽  
pp. 327-340 ◽  
Author(s):  
Bruce Calvert
Keyword(s):  
Markov Process ◽  
Thomson Effect ◽  
Journey Time ◽  
Routing Policy ◽  
Long Run ◽  
Service Rates ◽  
Pass Through ◽  
Queues In Parallel

Suppose customers pass through a network of two queues in parallel. A statedependent routing policy gives individuals their quickest journey. The Downs-Thomson effect is any increase in the long-run expected journey time caused by an increase in the service rates. This effect may occur.

scholarly journals Optimal Multiserver Scheduling with Unknown Job Sizes in Heavy Traffic

2021 ◽  
Vol 48 (3) ◽  
pp. 136-137
Author(s):  
Ziv Scully ◽  
Isaac Grosof ◽  
Mor Harchol-Balter
Keyword(s):  
Response Time ◽  
Optimal Policy ◽  
Heavy Traffic ◽  
Single Server ◽  
Mean Response Time ◽  
Scheduling Policy

We consider scheduling to minimize mean response time of the M/G/k queue with unknown job sizes. In the singleserver k = 1 case, the optimal policy is the Gittins policy, but it is not known whether Gittins or any other policy is optimal in the multiserver case. Exactly analyzing the M/G/k under any scheduling policy is intractable, and Gittins is a particularly complicated policy that is hard to analyze even in the single-server case.

Customer routing to different servers with complete information

1989 ◽  
Vol 21 (04) ◽  
pp. 861-882 ◽  
Author(s):  
Zvi Rosberg ◽  
Parviz Kermani
Keyword(s):  
Complete Information ◽  
Service Rate ◽  
Dependent Rate ◽  
Routing Policy ◽  
State Dependent ◽  
Long Run ◽  
Ideal Situation ◽  
Ideal System ◽  
Holding Cost ◽  
Routing Policies

In this paper we consider a queueing system having n exponential servers, each with its own queue and service rate. Customers arrive according to a Poisson process with rate λ, and upon arrival each customer must be routed to some server's queue. No jockeying amongst the queues is allowed and each server serves its queue according to a first-come-first-served discipline. Each server i, 1 ≦ i ≦ n, provides service with a state-dependent rate μ (i)(k), k = 0, 1, …. In addition, at every queue i, there is a deterministic holding cost which occurs at rate h (i)(k) while there are k customers at the queue. An admissible routing policy is a policy that assigns each arriving customer to one of the queues. A decision at time t may be randomized and dependent on the queue lengths and decisions till time t . An optimal routing policy is an admissible policy that minimizes the long-run average holding cost. In this study, we bound the optimal cost from below, by considering an ideal system, where each server optimally selects a given proportion of customers, irrespective of other servers' selections. From this ideal system we construct a class of admissible routing policies, the overflow routing class, that approximates the ideal situation for each server. Finally, we evaluate the policies and compare them to the lower bound.

scholarly journals DYNAMIC ROUTING OF CUSTOMERS WITH GENERAL DELAY COSTS IN A MULTISERVER QUEUING SYSTEM

2009 ◽  
Vol 23 (2) ◽  
pp. 175-203 ◽  
Author(s):  
Nilay Tanik Argon ◽  
Li Ding ◽  
Kevin D. Glazebrook ◽  
Serhan Ziya
Keyword(s):  
Lagrangian Relaxation ◽  
Numerical Study ◽  
Heavy Traffic ◽  
Significant Advance ◽  
Greedy Heuristic ◽  
Single Server ◽  
Long Run ◽  
Central Controller ◽  
Routing Policies ◽  
The Cost

We consider a network of parallel service stations each modeled as a single-server queue. Each station serves its own dedicated customers as well as generic customers who are routed from a central controller. We suppose that the cost incurred by a customer is an increasing function of her time spent in the system. In a significant advance on most previous work, we do not require waiting costs to be convex, still less linear. With the objective of minimizing the long-run average waiting cost, we develop two heuristic routing policies, one of which is based on dynamic programming policy improvement and the other on Lagrangian relaxation. In developing the latter policy, we show that each station is “indexable” under mild conditions for customers’ waiting costs and also prove some structural results on the admission control problem that naturally arises as a result of the Lagrangian relaxation. We then test the performance of our heuristics in an extensive numerical study and show that the Lagrangian heuristic demonstrates a strong level of performance in a range of traffic conditions. In particular, it clearly outperforms both a greedy heuristic, which is a standard proposal in complex routing problems, and a recent proposal from the heavy traffic literature.

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

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