SEVERANCE PAY AGREEMENT

Exhibit 10.2

SEVERANCE PAY AGREEMENT

This agreement is entered into by and between Avici Systems Inc. (the “Company”) and William Leighton (“you”) effective as of March 15, 2006.

SEVERANCE PAY

You will receive severance pay if you are terminated from employment with the Company without Cause or if you resign for Good Reason.

The amount of the severance pay will be twelve (12) months of your base salary at the rate in effect on your separation date, less applicable taxes. In addition, you will continue to participate in the Company’s group health, dental, and vision insurance plans, and, to the fullest extent permitted by the plans and applicable law, the Company’s 401k plan and the Company-paid life insurance plan, at the levels in effect on your separation date, for up to twelve (12) months. During this continuation period, the Company will pay the same percentage of your monthly group health, dental, vision, and life insurance premiums that it pays for active employees. At the end of the twelve (12) month period, you will, to the fullest extent permitted by the plans and applicable law, be eligible to continue your group health, dental, and vision coverage for up to an additional eighteen (18) months under COBRA. If you elect COBRA coverage you will be solely responsible for the full premium amounts.

To receive severance pay, you will be required to sign a mutual release of claims (which will not require you to release any rights under this agreement, rights to indemnification or exculpation or rights under any applicable insurance policies, nor prohibit you from any form of future employment with a competitive entity) in a form reasonably acceptable to you and the Company. Severance pay will be paid in accordance with the Company’s regular payroll practices beginning promptly after your signed release of claims goes into effect.

STOCK OPTIONS

If you are terminated without Cause prior to a Change of Control, the vesting of your remaining unvested Company options will accelerate by six (6) months.

In the event of a Change of Control, you will receive accelerated vesting on 50% of your remaining unvested options.

If, in connection with or following a Change of Control, you are terminated without Cause or you resign for Good Reason, the vesting on all of your remaining unvested options will be accelerated such that 100% of your options will become fully vested.

DEFINITIONS; OTHER

A termination for “Cause” as used herein means your being terminated by the Company due to (a) willful misconduct or violation of Company policy which causes material harm

to the Company, (b) willful breach of an employment or other agreement with the Company which causes material harm to the Company, or (c) being convicted of any felony.

A resignation for “Good Reason” as used herein means you resign because, following or at the time of a Change of Control, (a) you are transferred to a different position or suffer a reduction in responsibility; (b) your compensation is decreased; (c) you are required to relocate more than fifty (50) miles from your work location immediately prior to the Change of Control; or (d) you are excluded from any material compensatory or benefit plan or arrangement made available to similarly situated employees of the acquiring party.

“Change of Control” as used herein means the closing of (a) the sale of the Company by merger, consolidation or purchase of outstanding capital stock in which the shareholders of the Company, as such, no longer own a majority of the outstanding equity securities of the Company or its successor; (b) any sale of all or substantially all of the assets of the Company, other than in a spin-off or similar transaction; or (c) any other acquisition or disposition of the business or assets of the Company, as determined by the Board.

Assignment. This agreement will be binding on and inure to the benefit of the parties and the Company’s successors and assigns.

Employment at Will. This agreement is not an employment contract. Nothing in this agreement modifies your status as an employee at will or guarantees employment for any length of time.

Entire Agreement; Modification; Governing Law. Except as otherwise provided herein, this agreement constitutes the only agreement between you and the Company with respect to the subject matter hereof, superseding in all respects any and all prior oral or written agreements or understandings pertaining to the subject matter hereof. This agreement may be amended or modified only in a writing signed by both you and the Company. Any dispute concerning this agreement will be governed by the internal laws of Massachusetts.